1. The amount of tea leaves in a can from a production line is normally distributed withm= 110 grams ands= 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be less than 105 grams? (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of tea leaves in a can from a production line is normally distributed withm= 110 grams ands= 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be greater than 105 grams? (Only include calculation and answer: 1 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of tea leaves in a can from a production line is normally distributed withm= 110 grams ands= 25 grams. A sample of 25 cans is to be selected. So, 95% of all sample means will be greater than how many grams? (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of tea leaves in a can from a production line is normally distributed withm= 110 grams ands= 25 grams. A sample of 25 cans is to be selected. So, the middle 70% of all sample means will fall between what two values? (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is __________. (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is less than 36.03 is __________. (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is __________. (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.95 and 35.98 oz. is __________. (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. So, the middle 95% of the sample means based on samples of size 36 will be between __________ and __________. (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. The mean of the sample is ________, while the standard deviation of the sample is __________. (3 pts)

Formula to solve problem

Excel

Hand calculation

1. To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. Construct a 90% confidence interval for the mean score of actuarial students in the special program (4pts)

Given

Formula to solve problem

Excel

Hand calculation

1. A hotel chain wants to estimate the mean number of rooms rented daily in a given month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms. During February, a sample of 25 days has a sample mean of 370 rooms. Construct a 99% confidence interval for the mean number of rooms rented daily in a given month. (4 pts)

Given

Formula to solve problem

Excel

Hand calculation

1. A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. Construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report. (only figure by hand not compatible with excel)(2pts)

Given

Formula to solve problem

Hand calculation