(5%)
1. A pollster selected 4 of 7 available people. How many different groups of 4 are possible?
nC_{r} = n! / ( r! (n - r)! )
nC_{r} = 7! / ( 4! (7-4)! )
nC_{r} = 35
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? 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)
First, state H0 & Ha
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)