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REY [17]
3 years ago
8

Social scientists discovered that 1,013 General Social Survey (GSS) respondents in 2010 watched television for an average of 3.0

1 hours per day, with a standard deviation of 2.65 hours per day. Answer the following questions, assuming the distribution of the number of television hours is normal.
Required:
a. What is the Z score for a person who watches more than 8 hr/day?
b. What proportion of people watch television less than 5 hr/day? How many does this correspond to in the sample?
c. What number of television hours per day corresponds to a Z score of +1?
d. What is the percentage of people who watch between 1 and 6 hr television per day?
Mathematics
1 answer:
melamori03 [73]3 years ago
4 0

Answer:

Following are the responses to the given question:

Step-by-step explanation:

Sample \ size = n = 1013\\\\\mu = 3.01\\\\\sigma = 2.65

For point a:

Using formula:

Z = \frac{(X - \mu)}{\sigma}\\\\X = 8\\\\Z = \frac{(8- 3.01)}{2.65} = 1.88\\\\

For point b:

P(X

For point c:

X=? \\\\Z = 1\\\\\text{Formula for X score:}\\\\X = \mu + Z \times \alpha\\\\X = 3.01 + 1\times 2.65 = 3.01 + 2.65 = 5.66

For point d:

P(1 \leq X \leq 6)=? \\\\P(1 \leq X \leq 6) = P(X \leq 6) - P(X\leq 1) = P(X< 6) - P(X

Z = \frac{(1 -3.01)}{2.65} = -0.758490566\\\\P(Z< -0.758490566) = 0.224078679\\\\P(X

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