Question

The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 14. A random sample of 300 salespeople was taken and the mean number of cars sold annually was found to be 69. Find the 92% confidence interval estimate of the population mean.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

Answer 1

Solution :

Given that,

Point estimate = sample mean =     =69

Population standard deviation =    = 14

Sample size n = 300

At 92% confidence level the z is ,

= 1 - 92% = 1 - 0.92 = 0.08

/ 2 =0.04

Z/2 = Z0.04= 1.75 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.75* (14 /   300)

= 1.4145
At 92% confidence interval estimate of the population mean
is,

- E < < + E

69- 1.4145<   < 69 + 1.4145

67.5855<   <70.4145

(  LCL =67.5855 ,UCL =70.4145 )