SOLUTION: 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 m

Algebra ->  Probability-and-statistics -> SOLUTION: 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 m      Log On


   

Question 1117595: 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 16.2 minutes
​,
and the standard deviation is 3.5 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 nequals
45
oil changes results in a sample mean time less than 15

​minutes?
​(a) Choose the required sample size below.
A.
The sample size needs to be greater than 30.
Your answer is correct.
B.
The normal model cannot be used if the shape of the distribution is unknown.
C.
The sample size needs to be less than 30.
D.
Any sample size could be used.
​(b) The probability is approximately nothing
.
​(Round to four decimal places as​ needed.)
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Most statisticians will say that as large a sample as one can get, but n=30 has been used because even a t-distribution will be within 2 per cent of normality.
t(df=44)=(xbar-mean)/s/sqrt(n)
=(15-16.2)/3.5/sqrt(45)
=-1.2*sqrt(45)/3.5
=-2.30
This is a probability of 0.0130