Answer:
a) 2.09167
b) 0.2
c) 130 correspondents
d) 5.38 hours per day
e) 69%
Explanation:
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Mean = 2.98hrs/day, Standard Deviation = 2.4
a) What is the Z score for a person who watches more than 8 hrs/day.
z = 8 - 2.98/2.4
= 2.09167
b) What proportion of people watch 5 hrs/day or more television?
z = 5 - 2.98/2.4
z = 0.84167
Determining the Probabilityvalue from Z-Table:
P(x<5) = 0.80001
The proportion of people watch 5 hrs/day or more television
P(x>5) = 1 - P(x<5) = 0.19999
Approximately = 0.2
c) How many does this correspond to in the sample?
From the question above, we are told that: there are 650 GSS respondents in 2006 watched television
Hence the proportion that corresponds to Question b is
0.2 × 650
= 130 correspondents
Therefore, 130 correspondents watch 5 hrs a day or more television
d) What number of television hours per day corresponds to a Z = +1.
z score formula is given as:
z = (x-μ)/σ
Z = +1
x = unknown
Mean = 2.98
Standard deviation = 2.4
Hence:
1 = x - 2.98/2.4
Cross Multiply
1 × 2.4 = x - 2.98
2.4 = x - 2.98
2.4 + 2.98 + x
= 5.38 hours per day.
e)What is the percentage of people who watch between 1 and 6 hours of television per day?
For x = 1
z = 1 - 2.98/2.4
z = -0.825
Probability value from Z-Table:
P(x= 1) = 0.20469
For x = 6
z = 6 - 2.98/2.4
z = 1.25833
Probability value from Z-Table:
P(x = 6) = 0.89586
The percentage of people who watch between 1 and 6 hours of television per day is calculated as:
P(x = 6) - P(x = 1)
0.89586 - 0.20469
= 0.69117
Converting to percentage,
0.69117 × 100%
= 69.117%
To the nearest whole number = 69%
Therefore, 69% of the people who watch between 1 and 6 hours of television per day