Question

Q#1

The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.10 years and a standard deviation of 2.00 years. Random samples of size 12 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.

Q#2

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces. Find the probability if the sample is just 1 cup.

Answer 1

SOLUTION:

(A) = 5.10

= 2

n=12 sampling distribution of sample mean =₌ =

_=5.10

sampling distribution of standard deviation = / n = 2/ 12=0.58

(B)

Solution :

Given that ,

mean = = 12

standard deviation = = 0.2

n = 9

= 12

= / n = 0.2/ 9=0.07

P( <12.1 ) = P(( - ) / < (12.1-12) / 0.07)

= P(z < 1.43)

Using z table

= 0.9236

2.

= 12

= / n = 0.2/ 1=0.2

P( <12.1 ) = P(( - ) / < (12.1-12) / 0.2)

= P(z < 0.5)

Using z table

= 0.6915