Reference no: EM131886916
1. One year consumers spent an average of $21 on a meal at a resturant. Assume that the amount spent on a resturant meal is normally distributed and that the standard deviation is $33.
Complete parts? (a) through? (c) below.
a. What is the probability that a randomly selected person spent more than
?$23??
?P(X>?$23?)=
?(Round to four decimal places as? needed.)
b. What is the probability that a randomly selected person spent between
?$13 and $20??
?P($13less than<X<?$20?)=
?(Round to four decimal places as? needed.)
c. Between what two values will the middle 95?% of the amounts of cash spent? fall? The middle 95?% of the amounts of cash spent will fall between X=?$
and
X=?$
2.According to a social media? blog, time spent on a certain social networking website has a mean of 16
minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 33
minutes. Complete parts? (a) through? (d) below.
a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 15.5 and 16.5 minutes?
?(Round to three decimal places as? needed.)
b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 15 and 16 minutes?
?(Round to three decimal places as? needed.)
c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 15.5 and 16.5 minutes?
?(Round to three decimal places as? needed.)
d. Explain the difference in the results of? (a) and? (c).
The sample size in? (c) is greater than the sample size in? (a), so the standard error of the mean? (or the standard deviation of the sampling? distribution) in? (c) is _________ than in? (a). As the standard error __________ values become more concentrated around the mean.? Therefore, the probability that the sample mean will fall in a region that includes the population mean will always ____________when the sample size increases.
3.A market researcher selects a simple random sample of n=100 users of a social media website from a population of over 100 million registered users. After analyzing the? sample, she states that she has? 95% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the meaning of this statement.
Choose the correct answer below.
A. There is a? 95% chance that a randomly selected registered user spends between 15 and 57 minutes on the site per day.
B. During any given day there is a? 95% chance that the mean time all registered users spent on the site was between 15 and 57 minutes.
C.Of the over 100 million registered? users, 95% of them spend between 15 and 57 minutes on the site per day.
D.One is? 95% confident that the true mean time all registered users spend on the site per day is between 15 and 57 minutes.
4.The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 126 hours. A random sample of 81 light bulbs indicated a sample mean life of 400 hours. Complete parts? (a) through? (d) below.
a. Construct a 95?% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95?% confidence interval estimate is from a lower limit of hours to an upper limit of hours.
?(Round to one decimal place as? needed.)
b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 460 hours? Explain. Based on the sample? data, the manufacture ________ the right to state that the lightbulbs have a mean life of 460 hours. A mean of 460 hours is ____________ standard errors _________ the sample? mean, so it is ______________that the lightbulbs have a mean life of 460 hours.
c. Must you assume that the population light bulb life is normally? distributed? Explain.
A. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.
B. No, since σ is known and the sample size is large? enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem.
C. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.
D. No, since σ is? known, the sampling distribution of the mean does not need to be approximately normally distributed.
d. Suppose the standard deviation changes to 99 hours. What are your answers in? (a) and? (b)?The 95?% confidence interval estimate would be from a lower limit of hours to an upper limit of hours.
?(Round to one decimal place as? needed.)
Based on the sample data and a standard deviation of 99 hours, the manufacturer ___________the right to state that the lightbulbs have a mean life of 460 hours. A mean of 460 hours is _____________ standard errors ____________ the sample? mean, so it is ___________ that the lightbulbs have a mean life of 460 hours.