Corporate Client

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

 where  0, 1 or 2

4 marks   a. Construct the probability distribution of the variable 

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

2 marks    b. Calculate the mean of this probability distribution.

4 marks    c. Calculate the standard deviation of this probability distribution.

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

2 marks    i. at least 1 automobile to a corporate client?

2 marks    ii. at most 1 automobile to a corporate client?

1 mark    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

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

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

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