A.C Neilson reported that children between the ages of 2 and 5 watch an average of...

A.C Neilson reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume that the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the numbers of hours they watch television will be greater than 26.3 hours.

Solutions

Expert Solution

Solution:

Given that ,

= 25

= 3

A sample of size n = 20 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 25

SD = = 3/20 = 0.67082039325

find the probability that the mean of the numbers of hours they watch television will be greater than 26.3 hours.

i.e. Find P( > 26.3)

P( > 26.3)

= P[( - )/ > (26.3 - )/]

= P[ ( - )/ > (26.3 - 25)/ 0.67082039325]

= P[Z > 1.9379255805]

= P[Z > 1.94]

= 1 - P[Z < 1.94]

= 1 - 0.9738 ( use z table)

= 0.0262

P( > 26.3) = 0.0262

orchestra answered 1 year ago

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