Hours of Watching TV

Question

QUESTION: In a recent study, it was found that in one town the number of hours that a typical 10-year-old child watches
television per week is normally distributed with a mean of 12 hours and a standard deviation of 1.5
hours. PLEASE WORK IT OUT FOR ME.

 

 

A. If Gary is a typical 10-year-old child in this town, what is the probability that he watches
between 9 and 14 hours of television per week?

 

B. How many hours of television per week does Gary need to watch in order for him to be in the top 10%?

 

C. What is the probability that Gary watches TV for more than 14 hours?

 

D. If a sample 35 10-year old children is asked how many hour of television they watch, what is the probability that their mean hours of television watching is less than 10 hours?

 

Answer 1

mean= 12

sd = 1.5

find z scores for 9 and 14

z =(14-12)/1.5 = 2/1.5 = 20/15= 4/3 = 1.333...

z = (9-12)/1.5 = -3/1.5 = -2

from -2 to 0 is .95/2 = 47.5% using the empirical rule

from 0 to 1.333 = 40.88% using z tables or a z calculator

add them

= 88.38% are between 9 and 14

top 10% use z tables or a z calculator

to get about 1.282

= (x-12)/1.5 solve for x

x= 12 + 1.282(1.5) = about 13.923 or more puts you in the top 10%

P(more than 14 hours) = about 10% or about 9.12% = 50-40.88