Question

In: Statistics and Probability

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

The shape of the distribution of the time required to get an oil change at a 20-minute oil-change facility is unknown.​ However, records indicate that the mean time is 21.1 minutes​, and the standard deviation is 4.9 minutes. Complete parts ​(a) through (c).

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

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

B. The sample size needs to be greater than or equal to 30.

C. Any sample size could be used.

D. The sample size needs to be less than or equal to 30.

​(b) What is the probability that a random sample of n=40 oil changes results in a sample mean time less than 20 minutes?

The probability is approximately ______

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

There is a​ 10% chance of being at or below a mean​ oil-change time of _____ minutes.

Solutions

Expert Solution

Given data :

mean time is 21.1 minutes​, and the standard deviation is 4.9 minutes.

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

Ans :B. The sample size needs to be greater than or equal to 30.

​(b) What is the probability that a random sample of n=40 oil changes results in a sample mean time less than 20 minutes?

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

n=40

InvNorm(0.10)= - 1.28

Ans:

orchestra answered 1 year ago
Next > < Previous

Related Solutions

The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 20?-minute ?oil-change facility is unknown.? However, records indicate that the mean time is 21.1 minutes?, and the standard deviation is 4.2 minutes. 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 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random? sample, there...
the shape of the distribution of the time required to get an oil change in a...
the shape of the distribution of the time required to get an oil change in a 15 minute oil change facility is on now. However, records indicate them me Tom is 16.8 minutes, and the center deviation is 4.4 minutes. a.) To compute probabilities regarding the sample mean using the normal model what size would be required? b.) what is the probability that a random sample of n equals 40 oil changes results in a sample mean time less than...
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 10​-minute oil-change facility is unknown. However, records indicate that the mean time is 11.8 minutes​, and the standard deviation is 4.9 minutes. Complete parts ​(a) through (c). ​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required? A. The sample size needs to be less than or equal to 30. B. Any sample size could be...
The shape of the distribution of the time required to get an oil change at a...
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 16.8 minutes​, and the standard deviation is 4.3 minutes. Complete parts​ (a) through​ (c) below. To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required? Choose the required sample size below. A. Any sample size could be used. B. The normal model cannot be...
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 20​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.4 minutes​, and the standard deviation is 4.5 minutes. ​(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 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample,...
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 20 ​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.1 minutes ​, and the standard deviation is 4.8 minutes . Complete parts ​(a) through ​(c). ​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required? A. The sample size needs to be less than or equal to 30. B. The sample...
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 20​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.4 minutes, and the standard deviation is 4.5 minutes. ​(b) What is the probability that a random sample of n =35 oil changes results in a sample mean time less than 20 ​minutes? The probability is approximately _______. ​(Round to four decimal places as​ needed.)
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 1010​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 11.6 minutes11.6 minutes​, and the standard deviation is 4.5 minutes4.5 minutes. Complete parts​ (a) through​ (c) below. Click here to view the standard normal distribution table (page 1). LOADING... Click here to view the standard normal distribution table (page 2). LOADING... ​(a) To compute probabilities regarding the sample mean using the...
The shape of the distribution of the time required to get an oil change at a...
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 16.3 minutes​, and the standard deviation is 4.3 minutes. Complete parts ​(a) through ​(c). ​(a) To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required? A. The sample size needs to be greater than or equal to 30. B. The normal model cannot be...
The shape of the distribution of the time required to get an oil change at a...
The shape of the distribution of the time required to get an oil change at a 10-minute oil change store is unknown. However, records indicate that the mean time to get an oil change at the store is 14 minutes with standard deviation of 3.2 minutes To compute probabilities regarding the sample mean using the normal distribution, what sample size is required? What is the probability that a random sample of 40 oil changes results in a sample mean time...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT