Answer:
a)2.09
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,
σ is the population standard deviation.
Mean = average of 2.98 hrs/day, Standard deviation = 2.4 hours.
a) What is the Z score for a person who watches more than 8 hrs/day.
z = (x-μ)/σ
= 8 - 2.98/2.4
= 2.09167
≈ 2.09
b) What proportion of people watch 5 hrs/day or more television?
z = (x-μ)/σ
= 5 - 2.98/2.4
= 0.84167
P-value from Z-Table:
P(x<5) = 0.80001
The proportion that watches 5 hrs/day or more television?
P(x>5) = 1 - P(x<5) = 0.19999
≈ 0.2
c) How many does this correspond to in the sample?
From the question we are told:
650 GSS respondents in 2006 watched television for an average of 2.98 hrs/day, with a standard deviation of 2.4 hours.
Hence, the proportion that corresponds to people who watch 5 hrs/day or more television form the samples is
0.2 × 650
= 130 correspondents.
d) What number of television hours per day corresponds to a Z +1.
z = (x-μ)/σ
+1 = x - 2.98/2.4
Cross Multiply
1 × 2.4 = x - 2.98
2.4 = x - 2.98
x = 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?
Step 1
For 1 hour
z = (x-μ)/σ
= 1 - 2.98/2.4
= -0.825
Probability value from Z-Table:
P(x = 1) = 0.20469
Step 2
For 6 hours
z = (x-μ)/σ
= 6 - 2.98/2.4
= 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
P(x = 6) - P(x = 1)
= 0.89586 - 0.20469
= 0.69117
Converting to percentage =
0.69117 × 100
= 69.117 %
Approximately = 69%