Question

(5) A random sample of 100 college graduates revealed that they worked an average of 5 years on the job before being promoted. The population standard deviation is 2.0 years.

(a) Using the 0.68 degree of confidence, what is the confidence interval for the population mean?

(b) Using the 0.95 degree of confidence, what is the confidence interval for the population mean?

Answer 1

5)

Solution :

Given that,

= 5

= 2

= 5

= / n = 2 / 100 = 0.2

Using Empirical rule,

(a)

P(  - < X <   + ) = 0.68

P(5 - 0.2 < X < 5 + 0.2) = 0.68

P(4.8 < X < 5.2) = 0.68

4.8 to 5.2

(b)

P(  - 2 < X <   + 2 ) = 0.95

P(5 - 2 * 0.2 < X < 5 + 2 * 0.2) = 0.68

P(4.6 < X < 5.4) = 0.68

4.6 to 5.4