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?
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?
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
3 marks a. at most half will be females?
3 marks b. more than 7 will be females?
3 marks c. fewer than 3 will be males?
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