the attention span of a two-year-old is exponentiallydistributed with a mean of about 7 minutes. Suppose werandomly survey 60 two-year-olds.

Part (a)

In words, define the random variable X.

the ages of the children with short attention spans

the number of two-year-oldchildren

the attention span, in minutes, of all children

the attention span, in minutes, of a two-year-old child

Part (b)

Give the distribution of X.
X ~ ( , )

Part (c)

In words, define the random variable X.

the average number of two-year-old children

the average attention span, in minutes, for a sample of 60children

the average attention span, in minutes, for all children

the average age of children with short attention spans

Part (d)

Give the distribution of X.

(Round your standard deviation to two decimal places.)

X ~ ( , )

Part (e)

Before doing any calculations, which do you think will behigher?

the probability that an individual attention span is less than 8minutes

the probability that the average attention span of the 60children is less than 8 minutes

Part (f)

Calculate the probability that an individual attention span isless than 8 minutes. (Round your answer to four decimalplaces.)


Calculate the probability that the average attention span of the 60children is less than 8 minutes. (Round your answer tofour decimal places.)

Part (g)

Explain why the distribution for X

is not exponential.

According to the Law of Large Numbers, as the number of samplesincreases, the sample means tend to follow a uniformdistribution.

According to the Central Limit Theorem, as the number of samplesdecreases, the sample means tend to follow a normaldistribution.

According to the Central Limit Theorem, as the number ofsamples increases, the sample means tend to follow a normaldistribution.

According to the Law of Large Numbers, as the number of samplesdecreases, the sample means tend to follow a uniformdistribution.