How do we use computer to generate data?

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) = 

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?