Please answer all parts. Keep a copy of your solutions so you can check your wor

Question

Please answer all parts.

Keep a copy of your solutions so you can check your work when the answers are posted on Friday afternoon. Include your name and your answers only on the copy that you submit for possible extra credit points. The time that customers take to complete their transactions at an ATM mean 2 minutes and standard deviation of .6 minute. a. What is the probability that the average ATM-transaction time for a random sample of 50 customer will be between 1.8 and 2.25 minute? b. What is the probability that the total ATM-translation time for a random sample of 36 customer is less than one hour? c. there is a 90% probability that the average ATM-transaction time for a random sample of 50 customers is at least how many minutes?

Explanation / Answer

a) std error =std deviation/(n)1/2 =0.0849

hence P(1.8<X<2.25) =P((1.8-2)/0.0849<Z<(2.25-2)/0.0849)=P(-2.357<Z<2.9463)=0.9984-0.0092=0.9892

b)for 36 transaction mean time =36*2=72

and std deviation =0.6*(36)1/2 =3.6

hence P(X<60)=P(Z<(60-72)/3.6)=P(Z<-3.3333)=0.00043

c)for 90% ; z=1.28

hence minimum time =2-1.28*0.0849 =1.89 minutes

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