The amount of time Americans spend watching television is closely monitored by f

Question

The amount of time Americans spend watching television is closely monitored by firms such as A.C. Nielsen because this helps to determine advertising pricing for commercials. According to American Time Use Survey, the distribution of the variable “time spent watching television on a weekday” for American adults is skewed to the right with population mean of 2.35 hours per day and standard deviation of 1.93 hours per day.

A)Suppose an American adult is selected at random. What can be said about the probability that the person watches TV for at least 4.13 hours a day on a weekday?

B)Suppose a random sample of 36 adult Americans will be selected, the time spent watching television on a weekday will be recorded for each, and the sample mean time spent watching television on a weekday will be computed. What can be said about the probability that the sample mean time spent watching television on a weekday will be more than 3.18 hours?

Explanation / Answer

MEAN = 2.35

STANDARD DEV = 1.93

A) HERE WE NEED TO FIND P(X>4.13) =

For x = 4.13, z = (4.13 - 2.35) / 1.93 = 0.92

Hence P(x > 4.13) = P(z > 0.92) = [total area] - [area to the left of 0.92]

= 1 - 0.8212 = 0.1788

B) HERE WE JUST NEED TO CALCULATE THE P(X>3.18)

WE WILL APPLY THE SAME CONCEPT AS WE APPLIED ABOVE

For x = 3.18, z = (3.18 - 2.35) / 1.93 = 0.430

Hence P(x > 3.18) = P(z > 0.43) = [total area] - [area to the left of 0.43]

= 1 - 0.67 = 0.33

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