Question

The attention span of a two-year-old is exponentially distributed with a mean of about 9 minutes. Suppose we randomly survey 60 two-year-olds.

Give the distribution of

X.

(Round your standard deviation to two decimal places.)

Calculate the probability that an individual attention span is less than 11 minutes. (Round your answer to four decimal places.)


Calculate the probability that the average attention span of the 60 children is less than 11 minutes. (Round your answer to four decimal places.)

X

Answer 1

a) The probability that an individual attention span is less than 11 minutes is computed here as:

Therefore 0.7054 is the required probability here.

b) For 60 children, the distribution of the mean is obtained using Central limit theorem as:

Now the probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.9574 is the required probability here.