he shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.7 minutes, and the standard deviation is 4.6 minutes. Complete parts (a) through (c) below. (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the required sample size below. A. The sample size needs to be less than 30. B. Any sample size could be used. C. The sample size needs to be greater than 30. Your answer is correct. D. The normal model cannot be used if the shape of the distribution is unknown. (b) What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 15 minutes? The probability is approximately 0.00660.0066. (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager. (How to do it with a TI 84 Plus CE)

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Question

The shape of the distribution of the time required to get an oil change at a

15-minute

oil-change facility is unknown. However, records indicate that the mean time is

16.7 minutes,

and the standard deviation is

4.6 minutes.

Complete parts (a) through (c) below.

(a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required?

Choose the required sample size below.

The sample size needs to be less than 30.

Any sample size could be used.

The sample size needs to be greater than 30.

Your answer is correct.

The normal model cannot be used if the shape of the distribution is unknown.

(b) What is the probability that a random sample of

n=45

oil changes results in a sample mean time less than

minutes?

The probability is approximately

0.00660.0066.

(Round to four decimal places as needed.)

(c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform

oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, at what mean oil-change time would there be a 10% chance of being at or below? This will be the goal established by the manager.

(How to do it with a TI 84 Plus CE)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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