Question

Problem 1: The average diameter of pencils is normally distributed with a population standard deviation of 0.15 cm. A random sample of 25 pencils found the average diameter to be 0.95 cm.

Part A: Construct a 94% confidence interval for the population mean diameter.

Part B: Interpret the confidence interval. (1 pt)

Answer 1

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The normal distribution parameters are given below as :

Part A:

Mean = 0.95 cm

Stdev = 0.15 cm

n = 25

Part A:

The confidence interval of 94% is given by a Z of +/- 1.88

Mean +/- Z*stdev/sqrt(n)

= 0.95 +/- 1.88*.15/sqrt(25)

= 0.8936 to 1.0064

Part B:

IA 94% confidence interval is a range of values ( from 0.8936 to 1.0064) that you can be 94% certain contains the true mean of the population