Question

We discovered that 650 GSS respondents in 2006 watched television for an average of 2.98 hrs/day, with a standard deviation of 2.4 hours. Answer the following questions, assuming the distribution of the number of television hours is normal. What is the Z score for a person who watches more than 8 hrs/day. What proportion of people watch 5 hrs/day or more television? How many does this correspond to in the sample? What number of television hours per day corresponds to a Z +1. What is the percentage of people who watch between 1 and 6 hours of television per day? Please round to a whole number

Answer 1

Answer:

Given that,

Mean time =2.98 hrs,

Standard deviation =2.4 hrs.

(1)Z-score for (x=8)

Z= (x-)/

=(8-2.98)/2.94

Z=2.092.

Hence,Z score for a person who watches more than 8 hrs/day: Z=2.092.

(2)Properties of people who watch 5 hrs/day or more television P

Z-score for (x=5)

Z= (x-)/.

=(5-2.98)/2.94=0.842.

Hence P=P

From normal distribution table,

P=0.2000

Properties of people who watch 5 hrs/day or more television=0.20=20%.

(3)

Sample size=n=650.

NO.of people in the sample that proportion in part-2 corresponds=0.20*650=130.

(4)

Z= (x-)/

=(x-2.98)/2.94

1=(x-2.98)/2.94

x=2.98+2.4=5.38

Hence,mo,of television hours per day corresponds to a (Z=1)=5.38 hrs/day.

(5)

Percentage of people who watch between 1 and 6 hours of television per day =P

Z-score for (x=1):

Z= (x-)/.

=(1-2.98)/2.94=-0.825.

Z-score for (x=6):

Z= (x-)/.

=(6-2.98)/2.94=1.258

Hence P=

From normal distribution table,

=0.8959-0.2047=0.6912.

Percentage of people who watch between 1 & 6 hrs of television  per day=0.6912=69%.