Q3. (12 points) The amount of time that a drive through bank teller spends on a

Question

Q3. (12 points) The amount of time that a drive through bank teller spends on a customer is a random variable with   and .

A) A random sample of 5 customers is observed. Draw the sampling distribution of the sample mean label the mean and from the mean.

b) For a sample size of 5, what is the probability that the mean time at the teller’s window is less than 3 minutes? (Tip: Use your drawing in a to shade in the appropriate region.)

c) Now suppose random sample of 40 customers is observed. Draw the sampling distribution of the sample mean label the mean and from the mean.

d) For a sample size of 40, find the probability that their mean time at the teller’s window is less than 3 minutes.

sorry for the multiple questions, but they are all related to eachother in a sequence. if possible, don't do on paper, since it's really hard to see..thank you so much!

Explanation / Answer

a.
Mean ( u ) =3.5
Standard Deviation ( sd )=1.6/ Sqrt ( 5 ) = 0.7155
Number ( n ) = 5

b.
P(X < 3) = (3-3.5)/1.6/ Sqrt ( 5 )
= -0.5/0.7155= -0.6988
= P ( Z <-0.6988) From Standard NOrmal Table
= 0.2423                  

c.
Mean ( u ) =3.5
Standard Deviation ( sd )= 1.6/ Sqrt ( 40 ) = 0.253
Number ( n ) = 40

d.
P(X < 3) = (3-3.5)/1.6/ Sqrt ( 40 )
= -0.5/0.253= -1.9764
= P ( Z <-1.9764) From Standard NOrmal Table
= 0.0241                  

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