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.
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division. the product of 40 and distance to the finish line
Answer:
40*d
Step-by-step explanation:
The word product means multiplication, and here it is multiplying 40 and the distance(d).
Answer:
40x5
Step-by-step explanation:
How can I make the red segment less steep than the blue segment , and more steep than the green segment ?
A survey found that women's heights are normally distributed with mean 63.3 in. and standard deviation 2.7 in. The survey also found that men's heights are normally distributed with a mean 67.3 in. and standard deviation 2.8. Complete parts a through c below.
a) most of the live characters at an amusement park have height requirements with a minimum of 4ft 9in and a maximum of 6ft 4in find the percentage of women meeting the height requirement
the percentage of woment who meet the height requirement?
(round to two decimal places as needed)
b) find the percentage of men meeting the height requirement
the percentage of men meeting the height requirement
(round to two decimal places as needed )
c) If the height requirements are changed to exclude only the tallest 5% of men and the shortest 5% of women what are the new height requirements
the new height requirements are at least ___ in. and at most ___ in.
(round to one decimal place as needed)
a) The percentage of women meeting the height requirement is approximately 99.99%.
b) The percentage of men meeting the height requirement is approximately 99.95%.
c) The new height requirements are at least 58.5 inches and at most 71.8 inches.
a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.
First, we standardize the height requirement using the formula:
Z = (X - μ) / σ
where X is the value (height), μ is the mean, and σ is the standard deviation.
For the lower limit (57 inches):
Z_lower = (57 - 63.3) / 2.7 ≈ -2.33
For the upper limit (76 inches):
Z_upper = (76 - 63.3) / 2.7 ≈ 4.70
Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.
The percentage of women meeting the height requirement is approximately 99.99%.
b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:
For the lower limit (57 inches):
Z_lower = (57 - 67.3) / 2.8 ≈ -3.68
For the upper limit (76 inches):
Z_upper = (76 - 67.3) / 2.8 ≈ 3.11
Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.
The percentage of men meeting the height requirement is approximately 99.95%.
c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.
For men:
Z_upper_men = Z(0.95) ≈ 1.645
For women:
Z_lower_women = Z(0.05) ≈ -1.645
Using these Z-scores, we can calculate the new height requirements:
For the new lower limit:
X_lower = Z_lower_women * σ + μ
For the new upper limit:
X_upper = Z_upper_men * σ + μ
Substituting the values:
X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches
X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches
Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.
For more such question on percentage visit:
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a) The percentage of women meeting the height requirement is 99.99%.
b) The percentage of men meeting the height requirement is 99.95%.
c) The new height requirements are at least 58.5 inches and at most 71.8 inches.
a) For women meeting the height requirement:
Given: Mean (μ) = 63.3 in.
Standard Deviation (σ) = 2.7 in.
So, Minimum height requirement:
= 4 ft 9 in
= 4 * 12 + 9
= 57 inches
and, Maximum height requirement:
= 6 ft 4 in
= 6 * 12 + 4
= 76 inches
We will calculate the Z-scores for these heights using the formula:
Z = (x - μ) / σ
For the minimum height requirement:
[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33
For the maximum height requirement:
[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70
So, the the area between -2.33 and 4.70.
Thus, the percentage is 99.99%.
b) For men meeting the height requirement:
Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.
Minimum height requirement: 4 ft 9 in = 57 inches
Maximum height requirement: 6 ft 4 in = 76 inches
For the minimum height requirement:
[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68
For the maximum height requirement:
[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11
So, the area between -3.68 and 3.11.
Thus, the percentage is 99.95%.
c) For the new height requirements:
For men:
[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645
For women:
[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645
For the new lower limit:
[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]
For the new upper limit:
[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]
Substituting the values:
[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]
= 58.53 inches
and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]
= 71.78 inches
Therefore, the new height at least 58.5 inches and at most 71.8 inches.
Learn more about z score here:
https://brainly.com/question/31871890
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What’s the correct answer for this question?
Answer:
S ≈ 9.8
Step-by-step explanation:
Finding central angle of circle A first
S=r∅
6.5 = (4)∅
Central angle = 6.5/4
C A = 1.63(in radians)
Now finding Arc EF
S = r∅
S = (6)(1.63)
S = 9.75
S ≈ 9.8
please help :( really need answer
Answer:
Options (C) and (F)
Step-by-step explanation:
Polynomial function is,
f(x) = x³ - x² - 5x - 3
Possible rational roots of the given function will be = [tex]\frac{\pm1, \pm3}{\pm1}[/tex]
By putting x = -1
f(-1) = (-1)³ - (-1)² -5(-1) - 3
= -1 - 1 + 5 - 3
= 0
Therefore, x = -1 will a root of the given function.
Now we apply synthetic division to get the other roots,
-1 | 1 -1 -5 -3
↓ -1 2 3
1 -2 -3 0
Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).
Now we will find the roots of (x² -2x - 3).
x² - 2x - 3 = x² - 3x + x - 3
= x(x - 3) + 1(x - 3)
= (x + 1)(x - 3)
For roots of the function, f(x) = 0
(x + 1)(x - 3) = 0
x = -1, 3
Therefore, roots of the function are x = -1, 3
Options (C) and (F) are the answers.
Anyone know this at all?
Answer:
24.2
Step-by-step explanation:
You are given the hypotenuse and angle, and you want to find the length of the adjacent side.
The mnemonic SOH CAH TOA reminds you that the relation between angle and sides is ...
Cos = Adjacent/Hypotenuse
cos(41°) = x/32
x = 32·cos(41°)
x ≈ 24.2
A triangle with side lengths is 5,5,8 is what type of triangle
Answer:
isosceles triangle
Step-by-step explanation:
The volume of a triangular prism is increased by a factor of 8.
By what factor is the surface area of the figure increased?
o 2
o 4
016
o 24
Two barrels are mathematically similar
The smaller barrel has a height of [tex]h[/tex]cm and a capacity of 100 Liters
The larger barrel has a height of 90cm and a capacity of 160 Liters
-Work out the value of [tex]h[/tex]
Answer:
h ≈ 77 cm
Step-by-step explanation:
Let us convert the liters to cm³.
Smaller barrel
0.001 litres = 1 cm³
100 litres = 100000 cm³
Larger barrel
0.001 litres = 1 cm³
160 litres = 160000 cm³
For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.
This means
h³/90³ = 100000/160000
cube root both sides
h/90 = ∛100000 / ∛160000
h/90 = 46.4158883/54.2883523
cross multiply
54.2883523h = 46.4158883 × 90
54.2883523h = 4177.429947
divide both side by 54.2883523
h = 4177.429947/54.2883523
h = 76.9489175858
h ≈ 77 cm
What is the value of g-1(7)
Answer:
g-7
Step-by-step explanation:
Multiply the numbers
g-(1*7)
g-7
Answer:
5
Step-by-step explanation:
We know that g is an invertible function and so it must also be a one-to-one function.
This means that each input is paired with exactly one output and that each output is paired with exactly one input.
We know that g(a)=7g and g(5)=7. If the output of 7 is to be paired with exactly one input, then a must be equal to 5.
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (Consumer fraud and, 2008). (7.1.2)
State the random variable, population parameter, and hypotheses.
Answer:
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
Step-by-step explanation:
Information provided
n=1432 represent the random sample taken
X=321 represent the number of complaints
[tex]\hat p=\frac{321}{1432}=0.224[/tex] estimated proportion of complaints in 2007
[tex]p_o=0.23[/tex] is the value to verify
z would represent the statistic
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
What role did youth play in the Civil Rights Movement?
Answer:
they played the pivotal role
what is the common ratio of the geometric sequence below ?
-96,48,-24,12,-6...
Answer:
r = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The common ratio r is the ratio between consecutive terms in the sequence.
r = [tex]\frac{48}{-96}[/tex] = [tex]\frac{-24}{48}[/tex] = [tex]\frac{12}{-24}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex]
Answer:
-1/2 or b on edge
Step-by-step explanation:
If the size of the sample to be used in a particular test of attributes has not been determined by utilizing statistical concepts, but the sample has been chosen in accordance with random selection procedures
A) No inferences can be drawn from the sample.
B) The auditor has committed a nonsampling error.
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
D) The auditor will have to evaluate the results by reference to the principles of discovery sampling.
E) The auditor may or may not achieve the desired
Answer:
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
Step-by-step explanation:
In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.
This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean
Change the fraction1/5 to a percent
Answer:
Step-by-step explanation:
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =
Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
A study compared paired daytime and nighttime counts of sea trout, lake trout, and rainbow trout made by the same divers in six lakes during September 2015. Overall, they counted 127 trout during the day and 356 trout at night. The researchers speculate that trout counted at night were present during the daytime but were hidden from view. Biologists should consider that trout behavior and susceptibility to being seen might vary a great deal between daytime and nighttime, even during the summer. In some lakes, the majority of trout may not be seen during the daytime. Determine whether the study is an observational study or an experiment. Justify your answer with specific references to the information in the study.
Answer:
Observational Study
Step-by-step explanation:
An experimental study is a research study in which conditions are under the direct manipulation of the investigator. We use it to mainly test the efficacy of a medical, preventive, or therapeutic measure.
In an observational study, on the other hand, the researcher observes the effect without trying to influence the outcome in any way.
In this study, the researchers are trying to determine the paired daytime and nighttime counts of the species of fishes made by the same divers in six lakes during September 2015.
This is simply an Observational Study as nothing is done to influence the population count.
3. Set up an equation and use it to solve for x.
51°
(5x + 1)
Answer:
51 = 5x+1
x = 10
Step-by-step explanation:
The angles are vertical angles which means they are equal
51 = 5x+1
Subtract 1 from each side
51-1 = 5x+1-1
50 = 5x
Divide each side by 5
50/5 = 5x/5
10 =x
Answer:
10
Step-by-step explanation:
51 = 5x + 1
5x = 51 - 1
5x = 50
x = 10
Hope this helps!
(TEKS 2A.) EF has endpoints E (8,3) and F(-4,9). What is the distance of the given segment?
A 8.544
C 11.250
B 10.345
D 13.416
PLEASE HELP
Which of the following is an arithmetic sequence?
A: -2, 4, -6, 8, ...
B: -8, -6, -4, -2, ...
C: 2, 4, 8, 16, ...
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Volume of sphere = (4/3)πr³
= 4/3(3.14)(d/2)³
= 4/3(3.14)(7/2)³
= 4/3(3.14)(3.5)³
= 4/3(3.14)(42.875)
= (1.33)(3.14)(42.875)
= 179.5 cm³
Answer:
The answer is 179.5 cm^2
Parallelogram L M N O is shown. Angle M is (3 x minus 55) degrees, angle N is (5 y) degrees, and angle O is (2 x) degrees. In parallelogram LMNO, what are the values of x and y?
Answer:
x=55,y=14
Step-by-step explanation:
<M = <{opposite angles of a parallelogram are congruent and equal}
Hence 3x-55 = 2x=>3x-2x= 55 =>x=55
Simarly;
M+N=180°{ sum of angles in a parallelogram is 180°}
N= 180°-M=>N=180-(3x-55)=180-(3x55-55)= 180- 110=70°
N=70°=>5y=70=>y=70/5=14
therefore x=55,y=14
Answer:
55 and 14
Step-by-step explanation:
i just took the test
Please answer this correctly
Answer:
0
Step-by-step explanation:
No one is there which satisfies the condition
Answer:
0 or 0/9 of the club members
Step-by-step explanation:
The only part of the data of members that have logged more than 1 1/5 but less than 1 3/5 hours is the members that logged 1 2/5 hours. There are no members that have logged 1 2/5 hours so our answer is 0 or 0/9.
What is the answer ?
Answer:
[tex]f = \frac{1}{ {d}^{2} } [/tex]
The set of whales is a proper subset of the set of mammals.
Which choice is equivalent to the expression below?
root-81
A. 9i
B. i root9
C. root9i
D. -9
E. -root9
Answer: B
Step-by-step explanation:
Classify the following triangle .check all that apply
Answer:
acute and scalene
Step-by-step explanation:
Answer:no entiendo esta en ingles
Step-by-step explanation:
Hello! I'm stuck on this problem. Can someone help me? Thanks!
The model below represents an equation.
2 long x tiles and 3 square 1 tiles = 3 long x tiles
Which represent like terms in the model of the equation?
2 long x tiles and 3 square 1 tiles
2 long x tiles and 3 long x tiles
3 long x tiles and 3 square 1 tiles
1 long x tile and 1 square 1 tile
Answer:
Answer is B
Step-by-step explanation:
This is because you can combine both the green tiles. With the other options, you can't combine them.
(also I did the test )
Answer:
The answer is in ur head lololol
Step-by-step explanation:
Its b
Solve the following equation. x + 6 = x + x
Answer:
x = 6
Step-by-step explanation:
x + 6 = x + x
Combine like terms
x+6 =2x
Subtract x from each side
x+6-x = 2x-x
6 = x
It is believed that approximately 12% of the population of the United States is lefthanded. Suppose researchers suspect that the proportion of left-handed people is higher in certain states than the national average. The researchers conduct a sample of 200 randomly selected people in the state of Maine and find that 29 people in the sample are left-handed.
a. Write the null hypothesis and alternative hypothesis and define your parameter.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)
d. Is there strong evidence that the left-handed rate in the state of Maine is higher than the national average? Briefly explain how you know.
Answer:
Step-by-step explanation:
a. Null hypothesis: P = p
Alternatives hypothesis: P =/ p
Where P is the hypothesized population proportion and p is the sample proportion
b. Performing a test of proportions
Randomization: the sample was randomly selected in the study
The population size is at least 20 times as big as the sample size.
The sample includes both successes and failures with 29 success and 171 failures.
c. To perform the hypothesis test: we have to find the standard deviation first
Sd = sqrt[ P * ( 1 - P ) / n ]
where P is the hypothesized value of population proportion, n is the sample size.
Sd = √[0.12*(1-0.12)/200]
Sd = √[0.12*(0.88/200]
Sd = √[0.12*(0.0044)]
Sd = √0.000528
Sd = 0.023
Then we can find the z score
z = (p - P) / σ where p = 29/200 = 0.145
z = (0.145-0.12)/ 0.023
z = 0.025/0.023
z = 1.09
Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),
A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.
