Business Statistics Homework

Quiz #2

`Name________________________ Section No. _____________

(5%)

1. A pollster selected 4 of 7 available people. How many different groups of 4 are

possible?

10%

2. Your firm has a contract to make 2000 staff uniforms for a fast –food retailer. The

heights of the staff are normally distributed with a mean of 70 inches and a standard

deviation of 3 inches. What percentage of uniforms will have to fit staff shorter than

67inches? What percentage will have to be suitable for staff taller than 76 inches.?

a) 16% & 2.5%

b) 68% & 95%

c) 32% & 5%

(15%)

3. The industry standards suggest that 20% of new vehicles require warranty service

within the first year. A dealer sold 20 Nissans yesterday. Use equation for Binomial

Probability for part a) and Table II for part b) & c). Show work!

a) What is the probability that none of these vehicles requires warranty service? Use the

Binomial equation for P(X=0).

b) What is the probability that exactly one of these vehicles requires warranty service?

c) Determine the probability 3 or more of these vehicles require warranty service.

d) Compute the mean and std. dev. of this probability distribution.

(15%)

4. Allen & Associates write weekend trip insurance at a very nominal charge. Records

show that the probability a motorist will have an accident during the weekend and will

file a claim is quite small (.0005). Suppose Alden wrote 400 policies for the forthcoming

weekend. Compute the probability that exactly two claims will be filed using the equation

for Poisson Probability.

Note: The symbol λ is the mean (expected value) which we used as μ = np. So λ is

nothing more than the mean number of occurrences (successes = np) in a particular

interval.

Get the probability that the number of claims is at least 3 from Poisson Tables.

(10%)

5. Given a standard normal distribution, determine the following. Show Table Values

used in each part.

a) P(Z<1.4)

b) P(Z>1.4)

c) P(Z< -1.4)

d) P( - 0.50<Z<1.0)

e) P(0.50<Z<1.5)

15%

6. A company is considering offering child care for their employees. They wish to

estimate the mean weekly child-care cost of their employees. A sample of 10 employees

reveals the following amounts spent last week in dollars.

101 97 93 103 100 93 99 90 102 96

Develop a 95% confidence interval for the population mean. Interpret the result.

x =??, S=??, t 2/ =??, Range of  = (??)

15%

7. The National Safety Council reported that 56 % of American turnpike drivers are

men. A sample of 256 cars traveling southbound on the New Jersey Turnpike

yesterday revealed that 165 were driven by men. At the .01 significance level, can we

conclude that a larger proportion of men were driving on the New Jersey Turnpike

than the national statistics indicate? First, state H0 & Ha

HO: ??, Ha: ??

a) Is this a Z or t test? b) Test Statistic = ? c) Critical value = ? d) p-value = ? e) Reject Ho: (yes or no)

15%

8. Given the hypothesis: H0: μ≥18 & Ha: μ<18, a random sample of five resulted in

the following values: 17, 18, 20, 16, & 15. Using the .01 significance level, can we

conclude the population mean is less than 18?

a) Is this a Z or t test? b) Test statistic = ? c) Critical value = ? d) Reject Ho: (yes or no)