Question

1.) True or False? All continuous distributions are normally distributed.

2.)

What is the uniform distribution also known as?

Rectangular distribution

Box distribution

Polygon distribution

Square distribution

3.) An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.74 inch and 0.76 inch, respectively. Past experiences has indicated that the actual diameter of the ball bearing is approximately normally distributed, with a mean of 0.753 inch and a standard deviation of 0.004 inch. What is the probability that a ball bearing is: between the target and the actual mean?

0.2734

0.5000

0.2266

0.77266

4.)

Using the same information from question 3, what is the probability that the ball bearing is: between the lower specification limit and the target? (Format your probabilities to 4 decimal places)

0.00058

0.0006

0.2266

0.2260

5.)

Using the same information as question 3, what is the probability that the ball bearing is: above the upper specification limit? (Format your probabilities to 4 decimal places)

0.9599

1.7500

0.0401

1.0000

Answer 1

(1)

Correct option:

False

(2)

Correct option:

Rectangular distribution

(3)

To find P(0.75 < X < 0.753):

Z = (0.75 - 0.753)/0.004 = - 0.75

Table of Area Under Standard Normal Curve gives area = 0.2734

So,

Correct option is:

0.2734

(4)

To find P(0.74 < X < 0.75):

Case 1: For X from 0.74 to mid value:

Z = (0.74 - 0.753)/0.004 = - 3.25

Table of Area Under Standard Normal Curve gives area = 0.4994

Case 2: For X from 0.75 to mid value:

Z = (0.75 - 0.753)/0.004 = - 0.75

Table of Area Under Standard Normal Curve gives area = 0.2734

So,
P(0.74 < X < 0.75) = 0.4994 - 0.2734 = 0.2260

So,

Correct option is:

0.2260

(5)

To find P(X > 0.76):

Z = (0.76 - 0.753)/0.004 = 1.75

Table of Area Under Standard Normal Curve gives area = 0.4599

So,
P(X>0.76) = 0.5 - 0.4599 = 0.0401

So,

Correct option is:

0.0401