1. The mean amount of money that U.S. adults spend on food in a week is...

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1. The mean amount of money that U.S. adults spend on food in a week is $151 and the standard deviation is $49. Random samples of size 50 are drawn from this population and the mean of each sample is determined. (Adapted from Gallup) (a) Find the mean and standard deviation of the sampling distribution of sample means. (b) What is the probability that the mean amount spent on food in a week for a certain sample is more than $160? (c) What is the probability that the mean amount spent on food in a week for a certain sample is between $135 and $150? In Exercises 5 and 6, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. 5. A survey of U.S. adults found that 64% watch NFL football. You randomly select 20 U.S. adults and ask them whether they watch NFL football. Find the probability that the number who watch NFL football is (a) exactly 10, (b) less than 7, and (c) at least 15, and (d) identify any unusual events. Explain. (Source: Harris Interactive) 6. A survey of U.S. adults ages 25 and older found that 86% have a high school diploma. You randomly select 30 U.S. adults ages 25 and older. Find the probability that the number who have a high school diploma is (a) exactly 25. (b) more than 25, and (c) less than 25, and (d) identify any unusual events. Explain. (Source: U.S. Census Bureau) In Exercises 7-12, use the following information. The amounts of time Facebook users spend on the website each month are normally distributed, with a mean of 6.7 hours and a standard deviation of 1.8 hours. (Adapted from Nielsen) 9. Out of 800 Facebook users, about how many would you expect to spend between 2 and 3 hours on the website in a month? 10. What is the lowest amount of time spent on Facebook in a month that would still place a user in the top 15% of times? 1. The mean amount of money that U.S. adults spend on food in a week is $151 and the standard deviation is $49. Random samples of size 50 are drawn from this population and the mean of each sample is determined. (Adapted from Gallup) (a) Find the mean and standard deviation of the sampling distribution of sample means. (b) What is the probability that the mean amount spent on food in a week for a certain sample is more than $160? (c) What is the probability that the mean amount spent on food in a week for a certain sample is between $135 and $150? In Exercises 5 and 6, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. 5. A survey of U.S. adults found that 64% watch NFL football. You randomly select 20 U.S. adults and ask them whether they watch NFL football. Find the probability that the number who watch NFL football is (a) exactly 10, (b) less than 7, and (c) at least 15, and (d) identify any unusual events. Explain. (Source: Harris Interactive) 6. A survey of U.S. adults ages 25 and older found that 86% have a high school diploma. You randomly select 30 U.S. adults ages 25 and older. Find the probability that the number who have a high school diploma is (a) exactly 25. (b) more than 25, and (c) less than 25, and (d) identify any unusual events. Explain. (Source: U.S. Census Bureau) In Exercises 7-12, use the following information. The amounts of time Facebook users spend on the website each month are normally distributed, with a mean of 6.7 hours and a standard deviation of 1.8 hours. (Adapted from Nielsen) 9. Out of 800 Facebook users, about how many would you expect to spend between 2 and 3 hours on the website in a month? 10. What is the lowest amount of time spent on Facebook in a month that would still place a user in the top 15% of times?