Question

A mill cuts pieces of steel into parts that will later be used as the frame for front seats in an automotive plant. The steel is cut with a diamond​ saw, and the resulting parts must be within plus or minus±0.005 inch of the length specified by the automobile company. The data are shown in the accompanying table. The measurement reported is the​ difference, in​ inches, between the actual length of the steel part and the specified length of the steel part. Complete parts​ (a) and​ (b).

0.002

0.0005

-0.0025

-0.0015

0.0015

-0.002

-0.001

0.001

-0.0005

0.003

0.001

0.0005

0.0035

-0.0015

0.001

-0.004

0.0025

-0.0005

0.003

0.004

0.001

-0.003

0

-0.001

-0.001

0.0005

Decide whether the data appear to be approximately normally distributed by comparing data characteristics to theoretical properties. Based on the theoretical properties of the normal​ distribution, do the data appear to be approximately normally​ distributed?

A.Yes, the distribution of the data appears to closely resemble a normal distribution.

B. ​No, the mean and the median are significantly different.

C.​No, the range is less than 3 times the standard deviation.

D.No, the interquartile range is more than twice the standard deviation.

2)Decide whether the data appear to be approximately normally distributed by constructing a normal probability plot.

Answer 1

1) Option (A) -- Yes, the distribution of the data appears to closely resemble a normal distribution.is correct.

It can be verified that the mean and median are not significantly different, the range is not less than 3 times the standard deviation and the interquartile range is not less than 3 times the standard deviation.

The boxplot of the data shows that it has almost symmetric structure.

2) The normal probability plot is obtained and it is seen that most of the data points fall on the line in the normal probability plot. So, we can conclude that the data appear to be approximately normally distributed.

The answers are found out using R-software. The images and the required code along with output are attached below.