Question

The operations manager of a plant that manufactures tires wants to compare the actual inner diameters of two grades of tires, each of which is expected to be 575 millimeters. Samples of five tires from each grade were selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are shown below. Complete parts (a) through (c) below.

Grade Upper XGrade X	Grade Upper YGrade Y
565 570 576 579 587	nbsp 573 574 576 577 582

a. For each of the two grades of tires, compute the mean, median, and standard deviation.

The mean for Grade X

mm.

(Type an integer or a decimal.)

The mean for Grade Y is

(Type an integer or a decimal.)

The median for Grade X is

(Type an integer or a decimal.)

The median for Grade Y is

(Type an integer or a decimal.)

The standard deviation for Grade X is

mm.

(Type an integer or decimal rounded to two decimal places as needed.)

The standard deviation for Grade Y is

mm.

(Type an integer or decimal rounded to two decimal places as needed.)

b. Which grade of the tire is providing better quality? Explain. Choose the correct answer below.

A.

Grade X provides better quality. While the mean of Grade Y is closer to the expected mean, the standard deviation of Grade X is much smaller.

B.

Grade Y provides better quality. While the mean of Grade X is closer to the expected mean, the standard deviation of Grade Y is much smaller.

Your answer is correct.

C.

Grade Y provides better quality because its mean is much smaller.

D.

Grade X provides better quality because its mean is much smaller.

c. What would be the effect on your answers in (a) and (b) if the last value for Grade Y were

instead of

Explain. Choose the correct answer below.

When the fifth Grade Y tire measures

590590

mm rather than

mm, Grade Y's mean inner diameter becomes

mm, which is

larger

than Grade X's mean inner diameter, and Grade Y's standard deviation changes from

mm to

In this case, Grade X's tires are providing

better

quality in terms of the mean inner diameter.

(Round to two decimal places as needed.)

Answer 1

a. The mean for Grade X is = (565+570+576+579+587)/5 = 2877/5 = 575.4mm. (Ans).

The mean for Grade Y is = (573+574+575+576+577)/5 = 2882/5 = 576.4 mm. (Ans).

The middle for Grade X is = X_{(3)} = third request measurement = Middle

the vast majority of 5 perceptions = 576 mm. (Ans).

The middle for Grade Y is = Y_{(3)} = 576 mm. (Ans).

The standard deviation for Grade X is =

=8.4439 mm.

The standard deviation for Grade Y is = 3.5071mm.

b. Here, Grade Y gives the better quality. While the mean of

Evaluation X is nearer to the normal mean, the standard deviation

of Grade Y is a lot littler. Thus, Option (C) is the right

decision.

c. question not clear ( data insufficient ) please check it and post it again. thank you