Question

The days of training a new employee needs are normally distributed with a population standard deviation of 3 days and an unknown population mean. If a random sample of 23 new employees is taken and results in a sample mean of 18 days, use a calculator to find a 90% confidence interval for the population mean.

Answer 1

Answer:

90% confidence interval for the population mean

(16.971 , 19.029)

Step-by-step explanation:

Step(i):-

Given mean of the sample x⁻ = 18 days

Standard deviation of the Population 'σ' = 3 days

Given sample size 'n' =23

Step(ii):-

90% confidence interval for the population mean is determined by

$((x^{-} - Z_{0.10} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.10} \frac{S.D}{\sqrt{n} } )$

Critical value Z = 1.645

$((18 - 1.645 \frac{3}{\sqrt{23} } , 18+ 1.645 \frac{3}{\sqrt{23} } )$

(18 -1.029 , 18 + 1.029)

(16.971 , 19.029)

final answer:-

90% confidence interval for the population mean

(16.971 , 19.029)