The lifetime (in hours)of a 60-watt light bulb is a random variable that has a Normal distribution with$\sigma$= 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038.If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence,how many randomly selected 60-watt light bulbs should be tested to achieve this result?
A)13
B)97
C)165
D)42
E)Not within ± 2 of any of the above

Question

The lifetime (in hours)of a 60-watt light bulb is a random variable that has a Normal distribution with$\sigma$= 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of  = 1038.If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence,how many randomly selected 60-watt light bulbs should be tested to achieve this result?
A)13 
B)97 
C)165 
D)42 
E)Not within ± 2 of any of the above

Quizplus · Accepted Answer

The margin of error, E, is given by:
E = Z* (σ/√n)
where Z* is the z-score corresponding to the desired level of confidence (99% in this case) and σ is the standard deviation of the population (30 hours in this case).
To find the sample size, n, we rearrange the equation as follows:
n = (Z*σ / E)^2
Plugging in the given values, we get:
n = (2.576*30 / 6)^2 = 165.03
Since we can't have a fractional number of bulbs, we round up to the nearest integer and get:
n = 165
Therefore, we need to test 165 randomly selected 60-watt light bulbs to achieve a margin of error no larger than 6 hours with 99% confidence.

The Lifetime (In Hours)of a 60-Watt Light Bulb Is a Random