Question 41: A large car dealership claims that 54% of its customers are looking

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Question 41: A large car dealership claims that 54% of its customers are looking to purchase sport utility vehicles. A random sample of 65 customers is surveyed. What is the probability that less than 49% are looking to purchase an SUV? (3 points)

Question 42: The local nursery is waiting for its spring annuals to be delivered, and 28% of the plants ordered are daisies. If the first truck contains 220 plants packed at random, what is the probability that no more than 55 of the plants are daisies? (3 points)

Question 43: A popular restaurant claims that 31% of its customers order the daily special. A random sample of 150 customers is surveyed. What is the probability that the proportion of diners who ordered the special differs from the population proportion by less than 1.5%? (3 points)

Question 44: The management of a large grocery store was informed by a consumer market research company that 81% of shoppers are women. In order to gain information about spending habits, a random sample of 75 shoppers were surveyed. What is the probability that the proportion of women in the sample differs from the population proportion by more than 4%? (3 points)

Question 45: The AAA recently reported that 64% of trucks on the road are Ford 150’s. What is the probability that a random sample of 160 trucks will contain less than 89 Ford 150’s? (3 points)

Question 46: The average typist can type 96 words per minute with a standard deviation of 16 words. What is the probability that the average number of words typed by a random sample of 75 typists will exceed 100? (3 points)

Question 47: The US Park Service recently reported that on average 560 cars per day (with a standard deviation of 166) enter the Redwood National Park. What is the probability that a random sample of 90 days will find that between 590 and 575 cars enter the park? (3 points)

Question 48: It has been reported that the average lifespan of the sparrow is 18.35 years with a standard deviation of 9.26 years. What is the probability that a random sample of 425 sparrow’s life span will be less than 17.66 years? (3 points)

Explanation / Answer

41)

Percent of customers who are looking to purchase sport utility vehicles i.e p = 0.54 or 54%

sample size i.e n = 65

By assuming normal distrubtion for sample propotion

standard devaition of proportion of customers who are looking to purchase sport utility vehicles= p*(1-p)/n

= (0.54*(1-0.54)/65)0.5 = 0.0618

z value = (x-mean)/sd

z value for 49% or 0.49 is (0.49-0.54)/0.0618 = -0.809, corresponding probability using z table is 0.2093

so P(sample proportion <= 0.49 ) = 0.2093

probability that less than 49% are looking to purchase an SUV is 0.2093

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