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Answer:
Probability that a group of 4 Americans watch more than 400 hours of television per year is 0.3264.
Step-by-step explanation:
We are given that a nationwide census is conducted and it is found that the mean number of hours of television watched per year by Americans is 350 with a standard deviation of 220.
A group of 4 Americans is selected.
Let = <u><em>sample mean number of hours of television watched per year</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = 350
= standard deviation = 220
n = sample of Americans = 4
Now, the probability that a group of 4 Americans watch more than 400 hours of television per year is given by = P( > 400 hours)
P( > 400) = P(
>
) = P(Z > 0.45) = 1 - P(Z
0.45)
= 1 - 0.6736 = <u>0.3264</u>
The above probability is calculated by looking at the value of x = 0.45 in the z table which has an area of 0.6736.
Hence, the probability that a group of 4 Americans watch more than 400 hours of television per year is 0.3264.