Question

Question 9 (1.2 points) The GMAC Insurance company reported that the mean score on the National Drivers Test was 78.3 with a standard deviation of 3.3 points. The test scores are approximately bell shaped. Approximately 68% of all test scores were between two values A and B what is the value of A? Write only a number as your answer. Round to one decimal place. Your Answer: Answer Question 10 (1.2 points) In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is 19 with a standard deviation of 20 days. Assume the data to be approximately bell-shaped Approximately 95% of all customer accounts have the average number of days between two values A and B. What is the value of B? Write only a number as your answer Your Answer:

Answer 1

(Question 9) answer A=75.02

since the test score is approximately bell shaped, so A and B will be equi-distant from mean.

and we have to find A and B such that P(A<78.3<B)=0.68 and

corresponding P(z1<Z<z2)=0.68

or, P(Z<z2)-P(Z<z1)=0.68

or, 1-P(Z<z1)-P(Z<z1)=0.68 ( since the the score is bell shaped and symmetrical)

or, P(Z<z1)=(1-0.68)/2=0.16

or z1=-0.9945 and A=mean-0.9945*sd=78.3-0.9945*3.3=75.02 and

z2=0.9945 and B=mean-0.9945*sd=78.3+0.9945*3.3=81.58 and

(Question 10)

answer B=58.2

since the test score is approximately bell shaped, so A and B will be equi-distant from mean.

and we have to find A and B such that P(A<19<B)=0.95 and

corresponding P(z1<Z<z2)=0.95

or, P(Z<z2)-P(Z<z1)=0.95

or, 1-P(Z<z1)-P(Z<z1)=0.95( since the the score is bell shaped and symmetrical)

or, P(Z<z1)=(1-0.95)/2=0.025

or z1=-1.96 and A=mean-1.96*sd=19-1.96*20=-20.2 and

z2=1.96 and B=mean-1.96*sd=19+1.96*20=58.2 and