Question

The mass of a bearing manufactured in a factory is distributed normally with a mean of 14.91 grams and a standard deviation of 0.92 grams. Product specifications call for the bearing to have a mean mass of 14.96 grams within 0.1 gram.

1. What proportion​ (in decimal​ form) of the individual bearings are within​ specification?

2. Pistons that are too large can be reworked but pistons that are too small have to be scraped and recycled. What proportion of the bearings are​ scraped? ​ (Give answer in decimal​ form.)

3. 98.61% of the time the mass of the bearings are smaller than what​ value?

A random sample of 6 bearings is taken. The masses are measured and then averaged.

4. What is the standard deviation of the distribution of sample​ means?

5. What proportion​ (in decimal​ form) of these average values are less than 15.4517?

6. What proportion​ (in decimal​ form) of the average values are within the product​ specifications?

Answer 1

The mass of a bearing manufactured n a factory is distributed normally with

Product specification says that the bearing to have a mean mass between 14.86 and 15.06.

1) The proportion of individual bearing that are within specification is :

2) the proportion of the bearings that are​ scraped=

3) Let that value be A

4) the standard deviation of the distribution of sample​ means =

5) the proportion​ of these average values are less than 15.4517 =