1) At a certain restaurant in? Ohio, the number of minutes that diners spend at the table has a major impact on the profitability of the restaurant

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1) At a certain restaurant in? Ohio, the number of minutes that diners spend at the table has a major impact on the profitability of the restaurant. Suppose the average number of minutes that diners spend at a table for dinner at the restaurant is 97 minutes with a standard deviation of 18 minutes. Assume the number of minutes diners spend at their table follows the normal probability distribution. Complete parts a through d.

a. Calculate the probability that the average number of minutes that diners spend at their table for dinner will be less than 100 minutes using a sample size of 9 tables.

?(Round to three decimal places as? needed.)

2. According to the Bureau of Labor? Statistics, Americans spent on average ?$2, 913 in 2016 on entertainment. Assume the population standard deviation of this spending is $863. A random sample of 28 adults was selected and was found to have an average spending of?$2,725 on entertainment. Complete parts a and b.

a. Does this sample provide support for the conclusions of the BLS? poll?

There is a .... chance of observing a sample mean as low as ?$2 comma 7252,725. This probability is ? low not low enough? (0.05) to contradict the findings of the poll.

?(Type an integer or decimal rounded to three decimal places as?needed.)

3. The average weight of a professional football player in 2009 was 246.2 pounds. Assume the population standard deviation is 25pounds. A random sample of 32 professional football players was selected. Complete parts a through e.

a. Calculate the standard error of the mean. σ-x

4. According to a certain? organization, adults worked an average of 1,783 hours last year. Assume the population standard deviation is 370 hours and that a random sample of 50 adults was selected. Complete parts a through e below.

a. Calculate the standard error of the mean. sigma Subscript x overbarσxequals=n

?(Round to two decimal places as? needed.)

5. A college has 250 ?full-time employees that are currently covered under the? school's health care plan. The average?out-of-pocket cost for the employees on the plan is ?$11,910 with a standard deviation of ?$520. The college is performing an audit of its health care plan and has randomly selected 35 employees to analyze their? out-of-pocket costs.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be less than ?$1,860??

c. What is the probability that the sample mean will be more than ?$1,880??

d. What is the probability that the sample mean will be between?$1,930 and ?$1,960??

a. The standard error of the mean is nothing.

?(Round to two decimal places as? needed.)