Please 1-4

Problem 1:True or False

a) Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Define event A as {Both chips are red} and event B as {At least one of the chips is blue}.

Then, true or false: A = ~B

b) The expected value of a random variable must be one of the values in which the random variable can

result.

c) If two events, A and B, are mutually exclusive, then P(A and B)= P(A)*P(B).

d) The conditional probability of event A given that event B has occurred is written P(B | A).

e) If every sample point in event B is also a sample point in event A, then P(A | B)=1.

f) For any continuous probability distribution, P(x=c)=0 for all values of c.

g) The sampling distribution of a sample statistic calculated from a sample of n measurements is the

probability distribution of the statistic.

Problem 2: An insurance company sells hurricane damage insurance to a Florida homeowner for

$1,000/year. In a given year, there is a 95% chance of no damage, 4% chance of minor ($20,000)

damage, and a 1% chance of major ($80,000) damage.

A) Let x = the insurance company's profit. What is p(x)?

B) What is the probability that the insurance company will make a profit in any given year?

C) What is the company's expected yearly profit? Is this a profitable policy for the insurance

company?

Problem 3: In a survey, explain how the margin of error changes if a) the confidence level decreases; b)

the sample size increases; c) the variance in the data increases.

Problem 4: Heights of men follow a normal (unimodal and symmetric) distribution with a mean of 176

cm and a standard deviation of 7 cm. What is the percentage of men with heights:

A) between 169 and 177 cm?

B) greater than 190 cm?