Determine in each of the following situations whether the Central Limit Theorem

ID: 3154466 • Letter: D

Question

applies in order to conclude that X ~ N( mean, standard deviation/sqrt(n) ) . If CLT does not apply, then write NA

in the blank provided. If CLT does apply, then write X ~ N(mean, standard deviation/ sqrt(n) ) with values put in

for mean,standard deviation and n. if you know them. (4 pts)

(a) In a large population of college-educated adults, IQ’s have mean 118 and

standard deviation 20. Suppose 100 adults from this population are randomly

selected for a market research campaign. Do you know anything about the

sampling distribution of the sample mean IQ’s coming from repeatedly taking

samples of size 100 from the population of college-educated adults?

(b) The distribution of actual weights of 8 oz. wedges of cheddar cheese

produced by a certain company are Normal with mean 8.1 ounces and standard

deviation of 0.1 ounces. A simple random sample of four of these cheese wedges

is selected, and the sample mean weight of these cheese wedges is to be

computed. Do you know anything about the sampling distribution of the sample

mean weights coming from repeatedly taking samples of size 4 from the

population of weights?

weights of these bags should have a mean of = 16.0 oz. and a standard deviation

of = 0.4 oz. To monitor the process, forty bags are selected periodically and

their average weight is determined. Do you know anything about the sampling

distribution of the sample means coming from repeatedly taking samples of size

40 from the population of weights from these bags of cookies?

(d) The gasoline prices of a gallon of regular gasoline on a day last week in

Michigan had a mean of $2.00 and a standard deviation of $0.10. A simple

random sample of twenty-five gasoline stations is selected, and the sample mean

price of the gasoline prices from those stations computed. Do you know anything

about the sampling distribution of the sample means coming from repeatedly

taking samples of size 25 from the population of gasoline prices?

The sampling distribution of n samples with mean u and standard deviation s is a normal distribution with mean u and standard deviation s/sqrt(n)

a)sampling distribution =N(118,20/sqrt(100)) =N(118,2)

b)sampling distribution=N(8.1,0.1/sqrt(4))=N(8.1,0.05)

c)sampling distribution=N(16,0.4/sqrt(40))=N(16,0.0632)

d)sampling distribution=N(2,0.1/sqrt(25))=N(2,0.02)

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.