value 0.75 points Suppose that 20% of all subscribers to a nationally circulated
ID: 3370069 • Letter: V
Question
value 0.75 points Suppose that 20% of all subscribers to a nationally circulated business magazine eam an income in excess of $40,000. The magazine polls 15 subscribers at random to determine the income category into which each falls. What is the probability that none of the 15 subscribers eam more than $40,000? ANSWER: freport your answer to 3 decimal places, using conventional rounding rules) What is the probability that at least 3 but no more than 5 of the 15 subscribers earn more than $40,000? ANSWER: (report your answer to 3 decimal places, using conventional rounding rules) .What is the mean of this probability distribution? ANSWER (report your answer to 3 decimal places, using conventional rounding rules) What is the standard deviation of this probability distrbution? ANSWER: (report your answer to 3 decimal places, using conventional rounding rules)Explanation / Answer
It is binomial distribution, where n = 15, p = 0.20
a) P(X = 0) = 15C0 * (0.20)^0 * (0.80)^15 = 0.035
b) P(3 < X < 5) = P(X = 3) + P(X = 4) + P(X = 5)
= 15C3 * (0.20)^3 * (0.80)^12 + 15C4 * (0.20)^4 * (0.80)^11 + 15C5 * (0.20)^5 * (0.80)^10 = 0.541
c) mean = n * p = 15 * 0.20 = 3
d) Standard deviation = sqrt(n * p (1 - p))
= sqrt(15 * 0.20 * 0.80)
= 1.549
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