Question

The service life, in hours, of certain types of light bulbs can be modeled as a Normal random variable with mean ? and standard deviation ?=40 hours. If a random sample of N bulbs is taken. What is the minimum sample size required to ensure with a confidence level of 96%, that the true mean bulb life,?, is between less than 10 hours and more than 10 hours, with respect to the sample mean?

Answer 1

Solution :

Given that,

standard deviation = = 40

margin of error = E = 10

At 96% confidence level the z is ,

  = 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z/2 = Z0.02 = 2.054

Sample size = n = ((Z/2 * ) / E)2

= ((2.054 * 40) / 10)2

= 67

Sample size = 67