Question

Bird’s data analyst wants to model the sample mean distance of scooter rides. They plan to take a random sample of 41 scooter rides and to record the distance traveled on each ride (distance before the rider “releases” the scooter and the charge is processed). They decide it is reasonable to assume that the distribution of distances is approximately normal, but they don’t know the variance of the distribution. In the sample, the mean is 0.54 mile and the standard deviation is 0.1 mile.

a. If the population mean of the distribution of distances is 0.5, what is the probability that the sample mean will be 0.54 or larger? Four decimals, tolerance 0.0005

b. What is the exact probability that the sample mean will be within ½ of one sample standard deviation of the population mean? Four decimals

Answer 1

(a)

= 0.5

s = 0.1

n = 41

SE =s/

= 0.1/

= 0.0156

To find P( 0.54):

Z = (0.54 -0.50)/0.0156

= 2.5612

By Technology, Cumulative Area Under Standard Normal Curve = 0.9948

So,

P( 0.54):= 1 - 0.9948 = 0.0052

So,

Answer is:

0.0052

(b)

To find P(0.45 < < 0.55):

For = 0.45:

Z = (0.45 - 0.50)/0.1

= - 0.5

By Technology, Cumulative Area Under Standard Normal Curve = 0.3085

For = 0.55:

Z = (0.55 - 0.50)/0.1

= 0.5

By Technology, Cumulative Area Under Standard Normal Curve = 0.6914

So,

P(0.45 < < 0.55):= 0.6914 - 0.3085 = 0.3829

So,

Answer is:

0.3829