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Statistics / Statistical Techniques in Business and Economics 15 / Chapter 8 / Problem 44

Statistical Techniques in Business and Economics | 15th Edition | ISBN: 9780073401805 | Authors: Douglas Lind, William Marchal, Samuel Wathen

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The Oil Price Information Center of greater Houston reports the mean price per gallon of

Chapter 0, Problem 44

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QUESTION:

The Oil Price Information Center of greater Houston reports the mean price per gallon of regular gasoline is $3.00 with a population standard deviation of $0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between $2.98 and $3.02? c. What is the probability that the difference between the sample mean and the population mean is less than 0.01? d. What is the likelihood the sample mean is greater than $3.08?

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QUESTION:

The Oil Price Information Center of greater Houston reports the mean price per gallon of regular gasoline is $3.00 with a population standard deviation of $0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between $2.98 and $3.02? c. What is the probability that the difference between the sample mean and the population mean is less than 0.01? d. What is the likelihood the sample mean is greater than $3.08?

ANSWER:

Step 1 of 5

It is given that, the mean is and the standard deviation is .

Also, the number of samples taken is .

Step 5 of 5

a.)

To find the standard error of the mean in this experiment.

The standard error of the mean is given by,

.

Since and .

Then,

Hence, the standard error of the mean is 0.0285.

Step 3 of 5

b.)

To find the probability that the sample mean is between and .

The probability that the sample mean falls in a particular region is given by,

.

Since

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