STAT230 Week 8 Quiz 2 Complete Solution

Question: #1101

Quiz #2
`Name________________________ Section No. _____________
(5%)

1. A pollster selected 3 of 8 available people. How many different groups of 3 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 10% of new vehicles require warranty service within the first year. A dealer sold 15 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 2 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 I 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 0, 1, 3 & 4 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.
100 99 90 102 105 95 97 94 99 104
Develop a 90% 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≥20 & Ha: μ<20, a random sample of five resulted in
the following values: 18, 15, 12, 19, & 21. Using the .01 significance level, can we
conclude the population mean is less than 20?
a) Is this a Z or t test?
b) Test statistic = ?
c) Critical value = ?
d) Reject Ho: (yes or no)