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?
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
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