Answer:
z(65) = (65-64.2)/[2.81/sqrt(60)] = 0.8/(0.3279)
Step-by-step explanation:
Using the normal probability distribution and the central limit theorem, it is found that there is a 0.0154 = 1.54% probability that the mean height for the sample is greater than 65 inches.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It 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, which is the percentile of X. By the Central Limit Theorem, for samples of size n, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem:
Mean of 64.3 inches, thus [tex]\mu = 64.3[/tex]Standard deviation of 2.81 inches, thus [tex]\sigma = 2.81[/tex]Sample of 75, thus [tex]n = 75[/tex].The probability that the mean height for the sample is greater than 65 inches is 1 subtracted by the p-value of Z when X = 65, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{65 - 64.3}{\frac{2.81}{\sqrt{75}}}[/tex]
[tex]Z = 2.16[/tex]
[tex]Z = 2.16[/tex] has a p-value of 0.9846.
1 - 0.9846 = 0.0154
0.0154 = 1.54% probability that the mean height for the sample is greater than 65 inches.
A similar problem is given at https://brainly.com/question/24663213
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim
Answer:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Step-by-step explanation:
Information to given
n=735 represent the random sample taken
X=203 represent the number of people who have their prostate regularly examined
[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined
[tex]p_o=0.3[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:
Null hypothesis:[tex]p \geq 0.3[/tex]
Alternative hypothesis:[tex]p < 0.3[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
d. 10th e. 26th
Step-by-step explanation:
22-12=10
12+14=26
In 2 + In 8 - In 4
In 4
In 6
In 64
DONE
Answer:
ln 4
Step-by-step explanation:
plus(+) will become times and minus(-)will become divide. Combine all together as all are in terms of ln
ln (2x8)/4
=ln 4
Answer: In 4
Step-by-step explanation: edge 2021
In monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 6 day period had a standard error of 1.93. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places) 4.56
Answer:
1.54
Margin of error M.E = 1.54
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
Where M.E = margin of error
M.E = zr/√n
Given that
Standard deviation r = 1.93
Number of samples n = 6
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
M.E = (1.96×1.93/√6) = 1.544321633166
M.E = 1.54 (to 2 decimal place)
Margin of error M.E = 1.54
Please answer this correctly
Answer:
676
Step-by-step explanation:
lxw
14x35
4x24
6x15
676
£110 is divided between Sara, Gordon & Malachy so that Sara gets twice as much as Gordon, and Gordon gets three times as much as Malachy. How much does Sara get?
Answer:144 sweets
Step-by-step explanation:
If triangles DEF and NPQ are similar, what is the length of side d? As fraction or whole number.
The length of the side d would be 77/18.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
If triangles DEF and NPQ are similar, then
7/9 = d/ (11/2)
By cross multiply
9d = 7 x 11/2
d = 77/2 ÷ 9
d = 77/18
Thus, The length of the side d would be 77/18.
Learn more about ratios here:
brainly.com/question/186659
#SPJ2
A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 8 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store.
Answer: 0.401294
Step-by-step explanation:
z=x-μ/σ
z=20-22/8
z=-0.25
the probability for this z-score is 0.401294.
write any two numbers less than 15 , which has exactly four factors
Answer:
4 can be divided by 1 and 2
6 can be divided by 1 and 2
12 is wrong because it can be divided by 1,2, and 4 so it has 6 factors instead of 4
Step-by-step explanation:
During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?
Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00
Answer:
Exponential; $376.32
Step-by-step explanation:
Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.
The same would be true for the second month, so the overall multiplier for the two months is ...
(1.12)(1.12) = 1.12^2 = 1.2544
This makes the food bill for the second month amount to ...
1.2544 × $300 = $376.32
_____
As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.
If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.
If you vertically stretch the exponential function f(x)=2x by a factor of 3, what is the equation of the new function
Answer:
g(X)=3(2^x)
Step-by-step explanation:
A gum ball machine has 22 red 18 white 10 blue and 23 green. What chances of pulling out a red
Step-by-step explanation:
Total gum balls = 22 + 18 + 10 + 23 = 73
Probability of red gum = 22/73
On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?
(A) d = 6h
(B) d = 50h
(C) d = 48h
(D) d = 288h
Answer:
d = 48 h
Step-by-step explanation:
Lamar's distance traveled is directly proportional to the number of hours be drove.
So distance (d) ∝ hours (h)
Lamar traveled 288 miles in 6 hours
Since d ∝ h
then d = kh [ where k is the proportionality constant ]
if 288 = k × 6
k = =288/48
Therefore, equation will be d = 48 h will be the equation
he dot plot shows how many swimmers are in each line at a waterpark: Is the median or the mean a better measure of center for these data and why? Median, because the data are skewed and there is an outlier Median, because the data are symmetric and there are no outliers Mean, because the data are skewed and there is an outlier Mean, because the data are symmetric and there are no outliers
Answer:
Step-by-step explanation:
There's no plot, but I can give you this: Median is better with a large outlier, while mean is better for symmetry. Therefore, the correct answer would be either the first or fourth. Ofc, we can't see the plot so that's all I can give you.
Hope that helped,
-sirswagger21
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5? A. 1 over 13 B.1 over 8 C.5 over 13 D.5 over 8 PLEASE HURRY!!!!!!!!!!!!!!!!!
Answer:
B. 1 over 8
Step-by-step explanation:
To determine the probability of the spinner landing on 5, we need to first know what probability is,
probability = required outcome/all possible outcome
since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner. This implies that all possible outcome = 64
In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.
This implies that the required outcome = 8
but
probability = required outcome/all possible outcome
probability (of the spinner landing on 5) = 8/64 =1/8
Answer:
b
Step-by-step explanation:
The given line segment passes through the points (0, -3) and (-5, -4).
What is the equation of the line that is parallel to the given line and passes through the point (-2, 2)?
Answer:
y= 1/5x + 12/5
Step-by-step explanation:
Points: (0, -3) and (-5, -4)Line: y= mx+bSlope: m=(y2-y1)/(x2-x1)= (-4+3)/(-5-0)= -1/-5= 1/5Y-intercept: -3= 0*1/5+b ⇒ b= -3So the line is: y= 1/5x - 3Parallel line to this has same slope and passes through the point (-2, 2)
Its y- intercept is: 2= 1/5(-2)+b ⇒ b= 2+2/5= 12/5The required equation in slope- intercept form is:
y= 1/5x + 12/5What is the quotient if 3/8 of 30 is divided by 15/16 of 5/10?
Answer:
24
Step-by-step explanation:
That would be:
(3/8)(30)
---------------
(15/16)(1/2)
This can be reduced in various ways. First, divide that 30 by 15, obtaining:
6/8
-----------
1/32
Now invert the divisor (1/32) and multiply:
(6/8)(32/1)
This reduces to 6*4, or 24.
Use slope-intercept form to write the equation of a line
that has a slope of -3 and passes through the point
(1,-5).
Use the drop-down menus to select the proper value
for each variable that is substituted into the slope-
intercept equation
y =
X
DPM
m =
Answer:
y=-3x-2
Step-by-step explanation:
There is enough information to make a point-slope form equation that which we can convert into slope-intercept form.
Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]
We are given the slope of -3 and the point of (1,-5).
[tex]y-y_1=m(x-x_1)\rightarrow y+5=-3(x-1)[/tex]
Convert into Slope-Intercept Form:
[tex]y+5=-3(x-1)\\y+5-5=-3(x-1)-5\\\boxed{y=-3x-2}[/tex]
A student takes a multiple-choice test that has 11 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. (a) Find P (6). (b) Find P (More than 3). Round the answers to at least four decimal places.
Answer:
a) P(6) = 0.0097
b) P(More than 3) = 0.1611
Step-by-step explanation:
For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A student takes a multiple-choice test that has 11 questions.
This means that [tex]n = 11[/tex]
Each question has five choices.
This means that [tex]p = \frac{1}{5} = 0.2[/tex]
(a) Find P (6)
This is P(X = 6).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]
P(6) = 0.0097
(b) Find P (More than 3).
Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So
[tex]P(X \leq 3) + P(X > 3) = 1[/tex]
We want P(X > 3). So
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]
[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]
[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]
[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]
Then
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]
P(More than 3) = 0.1611
3/11 ÷ 3/11
and
9/10 ÷ 3/5
PLZ HELP ME
Answer:
3/11 divided by 3/11 is 1
9/10 divided by 3/5 is 1 1/2 (1.5)
Step-by-step explanation:
Answer:
1
1.5
Step-by-step explanation:
3/11 ÷ 3/11 = 1
9/10 ÷ 3/5 = 3/2 ≈ 1.5
A chemist needs a 20% solution of alcohol. How many liters of 15% solution should be added to 4 liters of 40% solution to get a 20% solution?
Answer:
16
Step-by-step explanation:
Let's call the liters x. We can write 0.15x + 0.4 * 4 = 0.2 (x + 4). When we solve for x we get x = 16 liters.
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
In the attached file
Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.
Answer:
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
Step-by-step explanation:
I am going to say that:
The speed of the first plane is x.
The speed of the second plane is y.
One plane is flying at twice the speed of the other.
I will say that y = 2x. We could also say that x = 2y.
Two airplanes leave an airport at the same time, flying in the same direction
They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.
If after 4 hours they are 1800 km apart, find the speed of each plane
After 1 hour, they will be x km apart. After 4, 1800. So
1 hour - x km apart
4 hours - 1800 km apart
4x = 1800
x = 1800/4
x = 450
2x = 2*450 = 900
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
3.
B
С
A
D
E
How many rays intersect at point o?
The tallest church tower in the Netherlands is the Dom Tower in Utrecht. If the angle of elevation to the top of the tower is 77° when 25.9 m from the base, what is the height of the Dom Tower to the nearest metre.
Answer:
Height of the Dom is 112.18 m.
Step-by-step explanation:
The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :
[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]
So, the height of the Dom is 112.18 m.
g A two-tailed test is one where: Select one: a. results in only one direction can lead to rejection of the null hypothesis b. negative sample means lead to rejection of the null hypothesis c. results in either of two directions can lead to rejection of the null hypothesis d. no results lead to the rejection of the null hypothesis
Answer:
c. results in either of two directions can lead to rejection of the null hypothesis.
Step-by-step explanation:
A two tailed test is performed when we want to test if there is statistically significant difference from the null state. That means that if the statistic value is significantly higher or significantly lower, we will reject the null hypothesis. Both tails have rejection areas.
What is the equation of a line with a slope of -2 that passes through the point(6,8)
Step-by-step explanation:
work is shown and pictured
Please answer this correctly
Answer:
21-25 = 4
26-30 = 3
Step-by-step explanation:
16-20 (4)= 17 17 17 18
21-25 (4)= 21 22 24 25
26-30 (3)= 26 27
30
31-35 (3)= 32 35 35
36-40 (5)= 36 37 37 38 39
41-45 (2)= 41 42
sorry it’s hard to see. please help!!!
Louis had 19 dogs. He feeds them with 38 pounds of biscuits. If there are 4 more
dogs, then how much more pounds of biscuit are needed?
Answer:
14
Step-by-step explanation:
Answer:
Which of these factors will affect the friction on a road
Step-by-step explanation:
