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# Statistics Questions

1. The ages (years) of three government officials when they died in office were

55, 44, and 60.

A. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples.

B. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution.

C. Compare the population range to the mean of the sample ranges. Choose the correct answer below.A.The population range is equal to the mean of the sample ranges.
B.The population range is equal to the age of the oldest official at the time of death and the mean of the sample ranges is equal to the youngest official at the time of death.
C.The population range is not equal to the mean of the sample ranges (it is also not equal to the age of the oldest official or age of the youngest official at the time of death).

D.The population range is equal to the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death.

D.Do the sample ranges target the value of the population range? In general, do sample ranges make good estimators of population ranges? Why or why not?

A. the Sample ranges do not target the population range, therefore, sample ranges do not make good estimators of population ranges.B the sample ranges do not target the population range, therefore, sample ranges make good estimators of population ranges.

2.Assume that adults have IQ scores that are normally distributed with a mean of 97.1 and a standard deviation 15.3.Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.)

The first quartile is _____

Trials in an experiment with a polygraph include 96 results that include 23 cases of wrong results and 73 cases of correct results. Use a 0.05significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

#### QUESTION CONTENT AREA BOTTOM

##### Part 1Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below.

A.H0:p=0.20
H1:p>0.20B.

H0:p=0.20
H1:p?0.20C.H0: p=0.80
H1:p?0.80
D.H0:p=0.80
H1:p<0.80

E.H0:p=0.20

H1:p<0.20F.H0:p=0.80

H1:p>0.80

##### Part 2

The test statistic is z=.(Round to two decimal places as needed.)

##### Part 3

The P-value is(Round to four decimal places as needed.)

##### Part 4 Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

_____H0.There _______sufficient evidence to support the claim that the polygraph results are correct less than 80%of the time.

When sevenbasketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name.

#### QUESTION CONTENT AREA BOTTOM

##### Part 1P(shoot free throws in alphabetical order)=

A classic counting problem is to determine the number of different ways that the letters of “success” can be arranged. Find that number. If the letters are mixed up in a random sequence, what is the probability that the letters will be in alphabetical order?

#### QUESTION CONTENT AREA BOTTOM

##### Part 1The number of different ways that the letters of “success” can be arranged is ______

(Type an integer or a simplified fraction.)

##### Part 2

The probability that the letters will appear in alphabetical order is____

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90%of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.7in. and a standard deviation of0.9in. FindP90.That is, find the hip breadth for men that separates the smallest 90%from the largest 10%.

#### QUESTION CONTENT AREA BOTTOM

##### Part 1The hip breadth for men that separates the smallest 90% from the largest 10%is

P90=________in.

Assume that when human resource managers are randomly selected, 64% say job applicants should follow up within two weeks. If 8 human resource managers are randomly selected, find the probability that exactly 3 of them say job applicants should follow up within two weeks.