The shape of the distribution of the time required to get an oil change at a 10

Question

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 11.4 minutes , and the standard deviation is 4.6 minutes .

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

(b) What is the probability that a random sample of n=35 oil changes results in a sample mean time less than 10 minutes?

(a) 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.

D.

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

(b) The probability is approximately

.

Explanation / Answer

a.
To compute probabilities regarding the sample mean using the normal model,
the minimum needs to be greater than 30.

b.
Mean ( u ) =11.4
Standard Deviation ( sd )=4.6
Number ( n ) = 35
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 10) = (10-11.4)/4.6/ Sqrt ( 35 )
= -1.4/0.7775= -1.8005
= P ( Z <-1.8005) From Standard NOrmal Table
= 0.0359

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