For each of the following cases, identify whether it is appropriate to apply the

Question

For each of the following cases, identify whether it is appropriate to apply the central limit theorem. If it is not appropriate, there will be exactly one violation to the theorem's requirements; identify that violation. a) A random sample of weights of six cotton balls are to be averaged. The average weight of the cotton balls is approximately normally distributed. b) The strengths of 50 magnets, determined by "pull force", are to be measured and averaged. All pull force measurements are independent. The true mean pull force for 30 of those magnets is actually different than the true mean pull force for the other 20. The average pull force of the 50 magnets is approximately normally distributed. c) The number of holes in a sheet of metal follows a binomial distribution. A random sample of 44 similar sheets were studied. The average number of holes per sheet of metal approximately follows a normal distribution. d) Lisa's laptop has 100% battery power at the start of Day 1. At the end of the day, Lisa records the percentage of battery power left before she charges it overnight This is repeated every day for two weeks. The recorded percentages are assumed to be a random sample. The average percentage of remaining battery power at the end of a day is approximately normally distributed. e) A customer service staff is responsible for answering 30 phone calls a day. The duration of each call is assumed to be independent of other calls. The duration's distribution is the same for all calls. The average duration of a call is approximately normally distributed.

Explanation / Answer

Result:

a). Not appropriate to apply.

Both sample size or population distribution are not given.

b).

Appropriate to apply.

(Sample size >30)

c).

Appropriate to apply

(Sample size >30)

d).

Not appropriate to apply.

Both sample size < 30 and population distribution is not normal.

e).

Appropriate to apply

(Sample size30)

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