Let the random variable x represent the number of automobiles…

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?
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
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?
Question 4 Use the standard normal distribution table to find
2 marks a. .
2 marks b. .
Question 5 Test scores on a university admissions test are normally distributed, with a mean of 500 and a standard deviation of 100.
4 marks a. What is the probability that a randomly selected applicant scores between 425 and 575?
4 marks b. What is the probability that a randomly selected applicant scores 625 or more?
2 marks c. What is the probability that a randomly selected applicant scores less than 500?
4 marks d. Twenty per cent of test scores exceed what value?
Question 6 4 marks 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,
4 marks a. what is the probability that the jury will reach the correct decision in at least 175 of the trials?
3 marks b. what is the probability that there will be fewer than 180 correct decisions?
4 marks c. What is the probability that there will be exactly 184 correct decisions?

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