The amount of time spent by North American adults watching television per week i

Question

The amount of time spent by North American adults watching television per week is normally distributed with a mean of 6 hours and a variance of 2.25.

(1)Suppose that Professor Tanaka is at the 4th percentile of the distribution. How long does she watch television per week?

Hint: convert to z-score, then find probability in standard normal tables , then calculate z-score, then convert to hours per week.
Answer: 3.37 hours.
(2) Suppose that you are going to take a random sample of 100 North American adults. What is the probability that more than 12 of them in the sample watch television for more than 8 hours?

(Hint: use normal approximation, remember the continuity adjustment factor; pick closest value)
answer: 0.125
I want to know how to get these two !!!!! Thanks in advance

Explanation / Answer

here std deviation =(2.25)1/2 =1.5

1)for 4 percentile ; z score =-1.7507 ( Note: if you want help in calculating z score ; please reply so that I may help)

hence corresponding score =mean +z*std devition =6-1.7507*1.5=3.37 Hours

2)

probability that someone watches TV for more then 8 hours =P(X>8)=1-P(X<8)=1-P(Z<(8-6)/1.5)1=-P(Z<1.3333)

=1-0.9082 =0.0918

from normal approximation of binomial distribution:

mean =np =1000*0.0918 =9.18

and std deviaiton =(np(1-p))1/2 =2.887

therefore probability that more than 12 of them in the sample watch television for more than 8 hours

=P(X>12)=1-P(X<=12) =1-P(Z<(12.5-9.18)/2.887)=1-P(Z<1.1515)=1-0.8752 =0.125

please revert for any clarification required.

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