To determine whether a metal lathe that produces machine bearings is

properly adjusted, a random sample of 25 bearings is collected and the

diameter of each is measured. The metal lathe has a historical standard

deviation of 0.015 for the diameter of the machine bearings.

a.) The sample mean, YBAR, of the 25 bearings will be calculated.

What is the probability that the sample mean, YBAR,

will be within 0.0075 of the metal lathe's true mean diameter, mu,

for the bearings being produced?

What did you assume in order to calculate this probability?

b.) The following random sample of 25 bearing diameters was obtained.

1.003 1.012 0.990 1.025 1.005

0.989 0.979 1.024 0.998 1.006

0.985 0.998 0.978 0.992 0.982

1.015 1.002 1.018 0.977 1.001

0.994 1.007 1.018 1.027 1.024

Calculate the following SAMPLE statistics:

mean, variance, standard deviation, and range.

Discuss/Read/Interpret your DATA displays.

How comfortable are you with your assumptions from part (a)?

c.) The target diameter of the bearings being produced is 1.

Using your answers from parts [(a and b)] to guide your logic,

do you believe the metal lathe is properly adjusted? Justify Your Answer.

This is what I have so far and I am just wondering if it is correct and how to continue onto part c:

a) z = ( x - μ ) / (σ÷√η) = -2.5

z = ( x - μ ) / (σ÷√η) = 2.5

P (0.9925 < x < 1.0075) = P (-2.5 < z < 2.5) = 0.9876

b) n= 25; Σx= 25.049; Σx²= 25.104; Σx³= 25.165; Σx^4= 25.232

Mean(μ)= 1.002; median= 1.0025; No Mode

σn-1 = 0.0157; (σn-1)²= 0.0002; CV% = 1.6%

range= 0.05; mid-range= 1.002; Probably right skewed.

Five number summary: Q0= 0.9775, Q1= 0.99, Q2= 1.0025, Q3= 1.018, Q4= 1.027, IQR= 0.028

Inner fence: 0.948 to 1.06, Outer fence: 0.906 to 1.102