The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with  = 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of  = 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 class=answers-bank-image d-inline rel=preload = 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) 13B) 97C) 165D) 42E) Not within ± 2 of any of the above

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The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with    = 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of    = 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 class=answers-bank-image d-inline rel=preload > = 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) 13B) 97C) 165D) 42E) Not within ± 2 of any of the above

Patricia Christopher · Accepted Answer

Final Answer : C, Explanation :  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)^2Plugging in the given values, we get:n = (2.576*30 / 6)^2 = 165.03Since we can't have a fractional number of bulbs, we round up to the nearest integer and get:n = 165Therefore, 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.

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