Question

The life in hours of a 75-W light bulb is known to be approximately normally distributed, with a standard deviation of σ = 25 hours. A random sample of 20 bulbs has a mean life of x¯ = 1014 hours.

Suppose we wanted to be 90% confidence that the error in estimating the mean life in hours is less than 10. What sample size should be used? NOTE: This requires an INTEGER.

Answer 1

Solution :

Given that,

Population standard deviation = = 25

Margin of error = E = 10

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 25 / 10)²

n = 16.91

n = 17

Sample size = 17