Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.7 years, and standard deviation of 2.9 years.

If you randomly purchase one item, what is the probability it will last longer than 4 years?

Answer 1

= 150

= 16

To find P(134< X< 198):

Case1: For X from 134 to mid value:
Z = (134 - 150)/16 = - 1

By 68 - 95 - 99.7 Rule, area = 0.68/2 = 0.34

Case 2: For X from mid value to 198:

Z = (198 - 150)/16 = 3

By 68 - 95 - 99.7 Rule, area = 0.997/2 = 0.4985

So,

P(134 < X < 198) =0.34 + 0.4985 = 0.8385

So,

Number of observations in the data set expected to be between the values 134 and 198 is given by:

0.8385 X 7500 = 6289 (the nearest single observation)Round to

So,

Answer is:

6289