Question

The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 17. A random sample of 470 salespeople was taken and the mean number of cars sold annually was found to be 69. Find the 95% confidence interval estimate of the population mean

Answer 1

Answer: Estimate mean is between 67.463 and 70.537

Explanation: A 95% Confidence interval of a sample mean:

mean ±
`z.(s)/(√(n) )`

α = 1 - 0.95

α = 0.05

α/2 = 0.025

z-score of α/2 = 1.96

Knowing that mean = 69, sd = 17 and there were 470 salespeople in the sample:

69 ±
`1.96.(17)/(√(470) )`

69 ±
`1.96.(17)/(21.68)`

69 ±
`1.96.0.78`

69 ± 1.537

lower limit: 69 - 1.537 = 67.463

upper limit: 69 + 1.537 = 70.537

With a confidence of 95%, the estimate mean number of cars sold is between 67.463 and 70.537