Answer:
[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]
And we can use the probability mass function and we got:
[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]
And replacing we got:
[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:
[tex]X \sim Binom(n=4, p=0.72)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X \geq 1)[/tex]
And we can use the complement rule and we got:
[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]
And we can use the probability mass function and we got:
[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]
And replacing we got:
[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by
P
(
x
)
=
p
(
1
−
p
)
x
−
1
where
p
is the probability of success on any one trial.
Assume that the probability of a defective computer component is 0.21. Find the probability that the first defect is found in the fifth component tested.
(Round answer to four decimal places.)
P
(
5
)
=
Answer:
M.
Step-by-step explanation:
A newborn baby whose Apgar score is over 6 is classified as normal and this happens in 80% of births. As a quality control check, an auditor examined the records of 100 births. He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
Answer:
The lower limit is 72.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is more than 2 standard deviations from the mean, it is unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]n = 100, p = 0.8[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
He would be suspicious if the number of normal births in the sample of 100 births fell below the lower limit of "usual." What is that lower limit?
2 standard deviations below the mean is the lower limit, so X when Z = -2.
Proportion:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2 = \frac{X - 0.8}{0.04}[/tex]
[tex]X - 0.8 = -2*0.04[/tex]
[tex]X = 0.72[/tex]
Out of 100:
0.72*100 = 72
The lower limit is 72.
Please answer this question I give brainliest thank you! Number 16
Answer:
4a
Step-by-step explanation:
The mean is found by adding all of the data set together and then dividing by the amount of individual pieces of data in the set.
(2+3+3+8) = 16
16/4=4
The answer is 4a.
what is the radius of the circle that has an area of [tex]81*x*pi[/tex] degrees
Answer:
R=9
Step-by-step explanation:
the formula for area of a circle is pi r squared
where r denotes the radius of the circle
equating the formula for area with the area of the circle provided
p\i r squared = 81 p\i
r squared = 81
r = radical 81
r =9 inches
According to market research, a business has a 75% chance of making money in the first 3 years. According to lab testing, of a certain kind of experimental light bulb will work after 3 years. According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7. 1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Here are some scenarios:
According to market research, a business has a 75% chance of making money in the first 3 years.
According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.
According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
1. Write the scenarios in order of likelihood from least to greatest after three years: the business makes money, the light bulb still works, and the car needs major repairs.
Answer:
The correct order in terms of likelihood from least to greatest would be
P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83
Car needs major repairs -> Business makes money -> Light bulb still works
Step-by-step explanation:
We are given probabilities of three different events.
According to market research, a business has a 75% chance of making money in the first 3 years.
P(Business) = 75% = 0.75
According to lab testing, 5/6 of a certain kind of experimental light bulb will work after 3 years.
P(Light bulb) = 5/6 = 0.83
According to experts, the likelihood of a car needing major repairs in the first 3 years is 0.7.
P(Car repair) = 0.70
We are asked to write these scenarios in order of likelihood from least to greatest after three years.
Which means that the events with least probability is less likely to occur.
The least probability is of car repair, then business and then light bulb.
So the correct order in terms of likelihood from least to greatest would be
P(Car repair) = 0.70 -> P(Business) = 0.75 -> P(Light bulb) = 0.83
Car needs major repairs -> Business makes money -> Light bulb still works
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional probability formula for event B given that event A occurs first by writing A and B in the blanks:
P ( _a0 | _a1) = P ( _a2 ∩ _ a3)
___________
P ( _a4)
Answer: [tex]\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}[/tex]
Step-by-step explanation:
The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)
[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}[/tex]
P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)
(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)
(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)
(4, 5), (4, 4), (4, 3), (4, 2), (4, 1)
(5, 4), (5, 3), (5, 2), (5, 1)
(6, 3), (6, 2), (6, 1)
= 30
P(B) = (1, 2), (2, 1) sum = 3
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) sum = 6
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3) sum = 9
(6, 6) sum = 12
= 12
P(A ∩ B) = (1, 2), (2, 1)
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3)
= 11
Use the following cell phone airport data speeds​ (Mbps) from a particular network. Find the percentile corresponding to the data speed 11.2 Mbps. 0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
Answer: the percentile is 74%
Step-by-step explanation:
The given data distribution is arranged in increasing order as:
0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.6 0.6 0.8 0.9 0.9 0.9 1.1 1.3 1.7 1.8 1.9 2.3 2.4 2.5 2.6 2.7 3.1 3.5 3.5 3.7 3.8 4.8 5.2 7.4 7.9 8.2 8.6 9.3 11.2 11.3 11.4 12.1 12.6 13.1 13.3 13.6 13.8 14.6 15.6 15.7 25.6
The total number of values given in the data is 50
Percentile = number of values in the distribution lesser than the given value × 100/ total number of values in the distribution
Considering the data speed of 11.2 Mbps, the number of data speed lower than 11.2 is 37
Percentile = (37 × 100)/50 = 74%
A fraction with a zero in the numerator equals
Answer:Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero. all have a fraction value of zero because the numerators are equal to zero.
Assignment
Use the function f(x) = 2x3 - 3x2 + 7 to complete the exercises.
f(-1) =
f(1) =
f(2)=
>
Answer:
The value of the function f(x) at x=a can be determined by substituting a instead of x into the function expression.
1. When x=-1, then
f(-1) = 2 * (-1)^3 - 3 * (-1)^2 + 7 = -2 - 3 + 7 = 2.
2. When x=1, then
f(1) = 2 * 1^3 - 3 * 1^2 + 7 = 2 - 3 + 7 = 6.
3. When x=2, then
f(-1) = 2 * 2^3 - 3 * 2^2 + 7 = 16 - 12 + 7 = 11.
Step-by-step explanation:
Answer:
f(−1) =✔ 2
f(1) = ✔ 6
f(2) =✔ 11
Step-by-step explanation:
There are 10 balls in a bag, 4 red balls and 6 black balls. If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag. Now you pick two times and each time you can only take one ball. What is the probability that you will pick two red balls
Answer:
The probability of selecting two red balls is 0.132.
Step-by-step explanation:
In a bag there are 10 balls in a bag, 4 red balls and 6 black balls.
The conditions of selecting a ball are:
If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag.It is also provided that only one ball can be picked at a time.
Now, it is given that two balls are picked.
The number of ways to select a red ball in the first draw is: [tex]{4\choose 1}=4\ \text{ways}[/tex]
Compute the probability of selecting a red ball in the first draw as follows:
[tex]P(\text{First ball is Red})=\frac{{4\choose 1}}{{10\choose 1}}=\frac{4}{10}=0.40[/tex]
Now as a red ball is selected it will not be replaced.
So, there are 9 balls in the bag now.
The number of ways to select a red ball in the second draw is: [tex]{3\choose 1}=3\ \text{ways}[/tex]
Compute the probability of selecting a red ball in the second draw as follows:
[tex]P(\text{Second ball is Red})=\frac{{3\choose 1}}{{9\choose 1}}=\frac{3}{9}=0.33[/tex]
Compute the probability of selecting two red balls as follows:
[tex]P(\text{Two Red balls})=P(\text{First ball is Red})\times P(\text{Second ball is Red})[/tex]
[tex]=0.40\times 0.33\\\\=0.132[/tex]
Thus, the probability of selecting two red balls is 0.132.
Solve for x: 3x - 5 = 2x + 6.
Your answer
Answer:
3x-5=2x+6
x-5=6
x=11
Select all of the following statements that are true:
A. Random samples only generate unbiased estimates of long-run proportions, not long-run means.
B. You shouldnt take a random sample of more than 5% of the population size.
C. There is no way that a random sample of 100 people can be representative of all adults living in the United States.
D. If this question is voted out, the alternate option is "larger samples are always better than smaller samples, regardless of how the sample was collected."
E. Nonrandom samples are always poor representations of the population
Answer:
B. You shouldnt take a random sample of more than 5% of the population size.
Step-by-step explanation:
B. You shouldnt take a random sample of more than 5% of the population size. This is True, so as to avoid the research analysis to be more complex to interpret and analyzed
However, the following are not true statements:
A. Random samples only generate unbiased estimates of long-run proportions, not long-run means. This is False, as there may be sampling error, when picking the sample, which will lead to bias estimates in the long run proportions
C. There is no way that a random sample of 100 people can be representative of all adults living in the United States. This is False, as using the right factors such as gender, age, income, etc, in selecting the sample, 100 people is enough to use as sample of adults living in the United States
D. If this question is voted out, the alternate option is "larger samples are always better than smaller samples, regardless of how the sample was collected." This is False, larger samples are not always better than smaller samples. In fact, they are often difficult to analyze and interpret.
E. Nonrandom samples are always poor representations of the population: This is False, depending on the expected outcome of the research study. Some research studies required the research to use Nonrandom samples to reach verifiable conclusion.
what is 2/3 of 460? Just a little easy one for points
Answer:
2/3 * 460 = 306 and 2/3
Multiply 460 by 2/3 by first multiplying 460 by 2, then divide that by 3:
460 x 2 = 920
920 /3 = 306 2/3
The answer is 306 2/3
Indicate which of the following situations inferential statistics: a. An annual stockholders' report details the assets of the corporation. b. A history instructor tells his class the number of students who received an A on a recent exam. c. The mean of a sample set of scores is calculated to characterize the sample. d. The sample data from a poll are used to estimate the opinion of the population. e. A correlational study is conducted on a sample to determine whether educational level and income in the population are related. f. A newspaper article reports the average salaries of federal employees from data collected on all federal employees.
Answer:
The situations c, d and e are Inferential statistics.
Step-by-step explanation:
Inferential statistics is used to determine reasons for a situation or phenomenon. It helps to draw conclusions grounded on extrapolations, and is hence fundamentally dissimilar from descriptive statistics that only summarizes the data that has truly been measured.
Descriptive statistics are short-term descriptive coefficients that condenses a given data set, which can be a demonstration of the whole or a sample of a whole population.
All descriptive statistics are either central tendency measure or variability measure. Measures of central tendency define the epicenter position of a distribution for a data set.
From the provided situations the Inferential statistics are:
c. The mean of a sample set of scores is calculated to characterize the sample.
d. The sample data from a poll are used to estimate the opinion of the population.
e. A correlational study is conducted on a sample to determine whether educational level and income in the population are related.
Thus, the situations c, d and e are Inferential statistics.
The one that demonstrates inferential statistics would be:
c). The mean of a sample set of scores is calculated to characterize the sample.
d). The sample data from a poll are used to estimate the opinion of the population.
e). A correlational study is conducted on a sample to determine whether the educational level and income in the population are related.
Inferential StatisticsInferential statistics is denoted as the kind of statistics that is concluded through a small sample employed which will act as the representative of the larger population.
The smaller sample's characteristics are analyzed and deductions are made in general about the entire population.
The above statements exemplify these characteristics by calculating the mean of the sample population and performing a correlational examination.
Thus, options c, d, and e are the correct answers.
Learn more about "Statistics" here:
brainly.com/question/14318705
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
78.5 cm^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
A = pi (5)^2
A = 25pi
Letting pi = 3.14
A = 25(3.14)
A =78.5 cm^2
Letting pi be the pi button
A =78.53981634
Rounding to the nearest tenth
78.5
Answer:
78.5 cm²
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr²
We know the radius of the circle is 5 centimeters.
r=5
Substitute 5 in for r.
a=π(5²)
Evaluate the exponent. 5² is equal to 5*5, which equals 25.
a=π(25)
Multiply 25 and pi
a=78.5398163397
Round to the nearest tenth. The 3 in the hundredth place tells use to leave the 5 in the tenths place as is.
a≈78.5
Add appropriate units. Area always uses units², and the units in this case are centimeters.
a≈78.5 centimeters²
The area of the circle is about 78.5 square centimeters.
A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap. What is the equation in fraction form
Answer:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Step-by-step explanation:
The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.
[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]
There are two different solutions:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):
[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]
[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]
A jury pool has 15 men and 21 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of:_____
(a) all men
(b) all women
(c) 8 men and 4 women
(d) 6 men and 6 women
Give all answers accurate to four decimal places.
Answer:
(a) all men = 3.6351 * 10^ -7
(b) all women = 2.3483* 10^ -4
(c) 8 men and 4 women = 0.0308
(d) 6 men and 6 women= 0.2170
Step-by-step explanation:
A jury pool has 15 men and 21 women, from which 12 jurors will be selected.
Total = 36 people
Probability of
(a) all men
= 15C12/36C12
= 455/1251677700
= 3.6351 * 10^ -7
(b) all women
= 21C12/36C12
= 293930/1251677700
= 2.3483* 10^ -4
(c) 8 men and 4 women
=( 15C8 * 21C4)/36C12
= (6435*5985)/1251677700
= 38513475/1251677700
= 0.0308
(d) 6 men and 6 women
= (15C6 * 21C6)/(36C12)
= (5005*54264)/1251677700
= 271591320/1251677700
= 0.2170
Help asap giving branlist!!!
Answer:
Option 2
Step-by-step explanation:
The question states "the width of the rectangle is 4 less than half the length." Since we are looking for the value of w, w will be equal to the expression we create. We start with half the length and than subtract 4 from it. This is because it says 4 less than half the length, not half of 4-length or another variation. In many of these problems the best way to solve them is by working backwards.
Answer:
Option 2
Step-by-step explanation:
Translating these words into math, we get w = 1/2l - 4 which is Option 2.
Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
I need the answers for 21 and 22
Answer:
21.b
22.c
Step-by-step explanation:
idk how to explain it lol I did mental math
What’s the correct answer for this question?
Answer:
1)
Volume of pyramid = 1/3(Ab)(h)
Where Ab is the area of base, h is height
Volume of cone = 1/3(Ab)(h)
a) Their formula for finding volume is same. Also, their painting heads are same.
b) Pyramids have a tetragonal base while cones have a polygonal base
2) Pyramids
Volume of cone = (1/3) πr²h
Since Area of a circle = πr²
So
Volume of pyramid = (1/3)(A)(h)
So we can use the formula of a circle in cone's formula
Answer:
i dont know but i want points
Step-by-step explanation:
hehehe
Find the mode for the following distribution.
Number Frequency
16
3
20
5
24
9
28
7
32
7
36
5
40
3
24
28
32
28 and 32
Answer:
28 and 32
Step-by-step explanation:
they have the most
A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have five messages
Answer:
The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
Step-by-step explanation:
Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.
The random variable is approximated by the Poisson Distribution with parameter λ = 5.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]
Compute the probability that on a randomly selected day she will have five messages as follows:
[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]
[tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]
Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
The table shows ordered pairs of the function y=8-2x What is the value of y when x = 8?
Answer:-8
Step-by-step explanation:
8 - 2 × 8
8 - 16
-8
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line? (full problem attached)
Answer:
(0,34)
Step-by-step explanation:
For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!
Answer:
The answer is (0,34)
A meteorologist reports that the chance of snow is less
than 30%. The correct inequality to represent this
comparison is s < 30. The variable s represents the
likelihood of snow
Which numbers are solutions of the inequality?
Choose all that apply.
20%
35%
17%
30%
29
%
1.5%
Answer:
1, 3, 5, 6
Step-by-step explanation:
Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16
The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.
What are the solutions of the inequality?The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.
In other words, these percentages are less than 30% and can be rightly represented by the variable s.
Learn more about inequality here:
https://brainly.com/question/24372553
#SPJ2
m^2-3m+2/m^2-m. Simplify
Answer:
Step-by-step explanation:
factor out the numerator and demoninator
(m-2)(m-1)/m(m-1)
= (m-2)/m
Based on the type of equations in the system, what is the greatest possible number of solutions? StartLayout Enlarged left-brace 1st Row x squared + y squared = 9 2nd row 9 x + 2 y = 16 EndLayout
Answer:
2
Step-by-step explanation:
Given the system of equations:
[Tex]x^2+y^2=9\\9x+2y=16[/tex]
Comparing [Tex]x^2+y^2=9[/tex] with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2[/tex].
The first equation is an equation of a circle centred at (0,0) with a Radius of 3.
The second equation 9x+2y=16 is a straight line equation.
A straight line can only intersect a circle at a maximum of 2 points.
Therefore the greatest possible number of solutions to the equations in the system is 2.
Answer:
2
Step-by-step explanation:
and jj is gay of outer banks
A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of being hospitalized. When a hospitalization occurs, the loss is uniformly distributed on [0, 1]. When two hospitalizations occur, the losses are independent. Calculate the expected number of people in the car who are hospitalized, given that the total loss due to hospitalizations from the accident is less than 1.
Answer:
0.534
Step-by-step explanation:
p(0 losses) = 0.7² = 0.49
p(1 loss) = 2 x 0.3 x 0.7 = 0.42
p(2 losses) = 0.09
This is a conditional probability problem. If the number of people hospitalized is 0 or 1, then the total loss will be less than 1. However, if two people are hospitalized, the probability that the total loss will be less than 1 is 0.5. we need to exclude the 50% x 0.09 chance of a double loss costing more than 1. So
P(Cost < 1)
= 0.49 + 0.42 +0.045
= 0.955
P(0 losses | Cost < 1)
= P(0 losses and Cost < 1) / P(Cost < 1)
= 0.49 / 0.955 = 0.513
P(1 loss | Cost < 1)
= 0.42 / 0.955 = 0.440
P(2 losses | Cost < 1) = 0.045 / 0.955 = 0.047
Now take the expectation:
E[X] = (0)(0.513) + (1)(0.440) + (2)(0.047)
= 0.440 + 0.094
= 0.534
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 4 students' scores on the exam after completing the course: 12,7,13,11 Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The 80% confidence interval for the average net change is (8.596, 12.904).
Critical value t=1.638.
Step-by-step explanation:
First, we calculate the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{4}(12+7+13+11)\\\\\\M=\dfrac{43}{4}\\\\\\M=10.75\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{3}((12-10.75)^2+(7-10.75)^2+(13-10.75)^2+(11-10.75)^2)\\\\\\s=\dfrac{20.75}{3}\\\\\\s=6.92\\\\\\[/tex]
We have to calculate a 80% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=10.75.
The sample size is N=4.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.63}{\sqrt{4}}=\dfrac{2.63}{2}=1.315[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
The t-value for a 80% confidence interval and 3 degrees of freedom is t=1.638.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.638 \cdot 1.315=2.154[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 10.75-2.154=8.596\\\\UL=M+t \cdot s_M = 10.75+2.154=12.904[/tex]
The 80% confidence interval for the average net change is (8.596, 12.904).
