Question 1:

Let the random variable x represent the number of automobiles that a top salesperson will sell to a corporate client. The only possible values for are 0, 1 and 2, and the probabilities for each of these values may be calculated from the formula

P(x) = 0.5 - (x/6) where x = 0, 1 or 2

a. Construct the probability distribution of the variable

Note: Express your probabilities to 4 decimal places of accuracy.

b. Calculate the mean of this probability distribution.

c. Calculate the standard deviation of this probability distribution.

d. What is the probability that a randomly selected top salesperson will sell

i. at least 1 automobile to a corporate client?

ii. at most 1 automobile to a corporate client?

iii. exactly 1 automobile to a corporate client?

Question 2:

According to a recent study, 38% of all women will suffer a hip fracture because of osteoporosis by the age of 85. If six women aged 85 are randomly selected, what is the probability that

a. None of them will suffer (or has suffered) a hip fracture due to osteoporosis?

b. At least four of them will suffer (or have suffered) a hip fracture due to osteoporosis?

c. Fewer than two of them will suffer (or have suffered) a hip fracture due to osteoporosis?

Question 3:

Seventy per cent of the student body of a very large post-secondary institution is female. In a random sample of 12 students, what is the probability that

a. at most half will be females?

b. more than 7 will be females?

c. fewer than 3 will be males?

Question 4:

Use the standard normal distribution table to find

a. P(z > 2.00)

b. P(O < z < 1.75))

Question 5:

Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100.

a. What is the probability that a randomly selected applicant scores between 425 and 575?

b. What is the probability that a randomly selected applicant scores 625 or more?

c. What is the probability that a randomly selected applicant scores less than 500?

d. Twenty per cent of test scores exceed what value?

Question 6:

The life span of a DVD player produced by one major company is known to be normally distributed with a mean of 6.2 years. If 4.01% of these DVD players have a life span of more than 8 years, what is the standard deviation of the DVD player's life span?

Question 7:

It is estimated that, in jury trials, the jury will reach the correct decision (guilty or not guilty) 92% of the time. In 200 randomly selected jury trials,

a. what is the probability that the jury will reach the correct decision in at least 175 of the trials?

b. what is the probability that there will be fewer than 180 correct decisions?

c. What is the probability that there will be exactly 184 correct decisions?