A small electronics firm has 60 employees Ten of the employe

A small electronics firm has 60 employees. Ten of the employees are older than 55. An attorney is investigating a client\'s claim regarding age discrimination. The attorney randomly selects 15 employees without replacement and records the number of employees over age 55.

What is the probability distribution of X = the number of employees over age 55 in a sample of 15 selected without replacement?

Find the average number of employees over age 55 in the sample.

Find the standard deviation of the number of employees over age 55 in the sample.

Find the probability that at least 2 of the employees selected will be over age 55.

Find the probability that less than 2 of the employees selected will be over age 55.

Find the probability that at most 4 of the employees will be over age 55.

The number of fatalities resulting from automobile accidents for a 10 mile stretch of an interstate highway averages 1 per 100,000 automobiles. During a particular holiday weekend 500,000 automobiles traveled over the 10-mile segment. Using Poisson distribution, find the probability of:

No fatalities

3 fatalities

At least one fatality

If 10 percent of the bolts produced by a machine are defective, determine the probability that out of 6 bolts chosen at random, (a) 1, (b) 0, and (c) less than 2, bolts will be defective.

a. If 3 percent of the electric bulbs manufactured by a company are defective, find the probability that in a sample of 100 bulbs, (i) 0, (ii) 1, (iii) 2 bulbs will be defective. (Hint: Poisson distribution).

b. If 13 cards are chosen at random (without replacement) from an ordinary deck of 52 cards, find the probability that (i) 6 will be pictured cards, (ii) none will be pictured cards. (Hint: Hypergeometric distribution).

A bank is evaluating their staffing policy to assure they have sufficient staff for their drive up window during the lunch hour. If the number of people who arrive at the window in a 15 minute period has a Poisson distribution with
? = 5.

How many people are expected to arrive during the lunch hour?

b. What is the probability that no one will show up during the lunch hour of 12:00PM to 1:00PM?

Solution

he number of fatalities resulting from automobile accidents for a 10 mile stretch of an interstate highway averages 1 per 100,000 automobiles. During a particular holiday weekend 500,000 automobiles traveled over the 10-mile segment. Using Poisson distribution, find the probability of:

No fatalities

3 fatalities

At least one fatality

mean # of deaths over 500,000 autos, m = 5
P(k) = e^-m *m^k/k!

a. P(0) = e^-5 = 0.0067 <------ answer

b. P(3) = e^-5*5^3/3! = 0.1404 <------ answer

c. P(>0) = 1 - P(0) = 0.9933 <-----answer