Question

Suppose the lifetime of incandescent light bulbs has a mean of 1691.805 hours and a standard deviation of 79.1675 days. According to the Central Limit Theorem, what happens to the histogram of averages as n increases?

Question 6 options:

1)	The histogram will begin to look less like the normal curve.

2)	The histogram will begin to look more like the normal curve.

3)	Increasing n will not affect the histogram of averages.

4)	It depends on the mean and standard deviation.

5)	The histogram will begin to look more like the original distribution.

Suppose the lifetime of incandescent light bulbs has a mean of 1691.805 hours and a standard deviation of 79.1675 days. According to the Central Limit Theorem, what happens to the histogram of averages as n increases?

Question 6 options:

1)	The histogram will begin to look less like the normal curve.

2)	The histogram will begin to look more like the normal curve.

3)	Increasing n will not affect the histogram of averages.

4)	It depends on the mean and standard deviation.

5)	The histogram will begin to look more like the original distribution.

Answer 1

The correct answer is:
2) The histogram will begin to look more like the normal curve.

According to the central limit theorem, if X1,X2,...XN are a sequence of iid random variables with finite mean and finite non-zero variance , then the distribution of

as n tends to infinity.

In other words, the histogram of averages as n increases would start looking more and more like the normal curve.

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