2022-05-10

1. Airline passengers arrive randomly and independently at the passenger-screening facility

at a major international airport. The mean arrival rate is 10 passengers per minute.a) Compute the probability of no arrivals in a one-minute period.

b) Compute the probability that three or fewer passengers arrive in a one-minute period.

c) Compute the probability of no arrivals in a 15-second period.

d) Compute the probability of at least one arrival in a 15-second period.

A young boy asks his mother to get 5 Game-Boy cartridges from his collection of 10 arcade and 5 sports games. How many ways are there that his mother can get 3 arcade and 2 sports games?

1. At a particular factory, every product is inspected by two men. The first inspector catches 80% of the defectives and sends them back for repairs. All the remaining items are sent to a second inspector, who misses about 40% of the defectives that get past the first inspector.

Given that a product was found to be defective, what is the probability that it was found by the first inspector?

(d)

Compute

*P*(*x*≥ 2).*P*(*x*≥ 2) =How do we use computer to generate data?

A coin is tossed

5

times. Find the probability that

none

are

tails.

Let A and B be events with P(A) = 0.8, P(B) = 0.7, and P(A and B) = 0.08. Are A and B

independent?

Suppose x is a random variable with a normal distribution with a mean of 60 and a standard deviation of 5. Find:

a)P(x<65)

b)P(x>53)

A manufacturer claims that at most 20% of the items in a stock are defective.

To test this, 20 items are randomly selected from the product.

If at most 3 items are defective, then the manufacturer is statement is accepted.

If the true probability of an item being defective is 0.2.

Find the probability of accepting the manufacturer’s statement?

(Hint: use the Binomial Distribution)

When not interrupted artificially, the duration of human pregnancies can be described, we will assume, by a mean of nine months (270 days) and a standard deviation of one-half month (15 days).

Between what two times, in days, will a majority of babies arrive?

The probability of a randomly selected adult in one country being infected with a certain virus is

0.006.

In tests for the virus, blood samples from

11

people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.

Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value

tα/2,

(b) find the critical value

zα/2,

or (c) state that neither the normal distribution nor the t distribution applies.

Here are summary statistics for randomly selected weights of newborn girls:

n=277,

x=28.5

hg,

s=6.8

hg. The confidence level is

95%.

Consider all seven-digit numbers that can be created from the digits 0-9$0\text{-}9$ where the first and last digits must be even and no digit can repeat. Assume that numbers can start with 0$0$. What is the probability of choosing a random number that starts with 8$8$ from this group?