Statistics and Probability Answers

The president of Doerman Distributors, Inc., believes that 31% of the firm’s orders come from first-time customers. A random sample of 101 orders will be used to estimate the proportion of first-time customers.

1. What is the probability that the sample proportion will be between 0.21 and 0.41?

7. What is the probability that the sample proportion will be between 0.26 and 0.36?

Assume that the population proportion is 0.80

1. Compute the standard error of the sample proportion for a sample size of 1600.

2. ompute the standard error of the sample proportion for a sample size of 10.

A departmental store has a single cashier. During the rush hours, customers arrive at
the rate of 15 customers per hour. The average number of customers that can be
processed by the cashier is 18 per hour. Assume that the conditions for the use of
single-channel queuing model apply. What is the:
a) Probability that the cashier is idle?
b) Average number of customers in the queuing system?
c) Average time a customer spends in the system?
d) Average number of customers in the queue?
e) Average time a customer spends in the queue waiting for service?

A company assumes that 0.5% of the paychecks for a month was calculated incorrectly.
The company has 350 employees and exami
ned the payroll records from one month

Musquodoboit World Airways operates a fleet of small passenger planes. Like most major airlines it has a
problem with no-shows, people who make reservations, but don't show up for their flight or cancel at the
last minute. Their no-show rate is 20%, comparable to the industry average. One type of aircraft used by
MWA can accommodate up to 16 passengers.
a) If they accept 16 reservations, what is the probability that the plane departs with every seat filled (0 noshows)?

b) As is common in the industry, MWA overbooks its flights. For this size aircraft, it accepts up to 17
reservations. Suppose that MWA has accepted 17 reservations for a particular flight. What is the
probability that everyone who shows up will get a seat?

The average price per gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky. Use this price as the population mean, and assume that the population standard deviation is $0.20.

1. For a random sample of 64 service stations, find the standard deviation of the sampling distribution of the sample mean.

2. For a random sample of 100 service stations, find the standard deviation of the sampling distribution of the sample mean.

Business Week conducted a survey of graduates from 30 top MBA programs in the country. On the basis of the survey, assume that the (population) mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume that the standard deviation for male graduates is $40,000, and for the female graduates it is $25,000.

1. For a random sample of 64 female graduates, find the standard deviation of the sampling distribution of the sample mean.

2. For a random sample of 100 male graduates, find the standard deviation of the sampling distribution of the sample mean.

The College Board reported the following mean scores for three parts of the Scholastic Aptitude Test (SAT): Critical Reading 502; Mathematics 515; Writing 494. Assume that the population standard deviation on each part of the test is 100.

1. For a random sample of 64 test takers, find the standard deviation of the sampling distribution of the sample mean.

2. For a random sample of 100 test takers, find the standard deviation of the sampling distribution of the sample mean.

a company assumes that .5% of the paychecks for a month was calculated in correctly.The company has 350 employees and examined the payroll records from one month.define the variables of interest

Answer the following questions:

a. State the decision rule based on p-values for a two-sided hypothesis test at level α = 0.01.


b. Consider the following hypothesis test where (n = 100).

H0: µ = 50 α = 0.10
Ha: µ > 50

Suppose z = -2.20. Compute the p-value. Should H0 be rejected?



c. Consider the following hypothesis test where (n = 100).

H0: µ = 50 α = 0.05
Ha: µ < 50

Suppose z = -2.20. Compute the p-value. Should H0 be rejected?



d. Consider the following hypothesis test where (n = 100).

H0: µ = 50 α = 0.01
Ha: µ ≠ 50

Suppose z = -2.20. Compute the p-value. Should H0 be rejected?