Question

Survey reveals that children ages 2-5 on average watch an average of 25 hours of tv a week. Assume variable is normally distributed with stand. dev 3 hrs.

(a) If 20 children in age group are t be randomly selected find the probability the average hours per week watched exceed26.3 hrs.
(b) Find probability a child ages 2-5 watches over 26.3 hrs tv per week

Answer 1

To find the probability that the average hours per week watched exceed 26.3 hours, use the Z-score formula. The Z-value can be found using the sample mean, population mean, population standard deviation, and sample size. For part (b), use the same Z-value to find the probability of a child watching over 26.3 hours.

Step-by-step explanation:

To find the probability that the average hours per week watched exceed 26.3 hours, we can use the Z-score formula. The formula is:

Z = (X - μ) / (σ / √n)

Where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, X = 26.3, μ = 25, σ = 3, and n = 20. Plugging these values into the formula, we get:

Z = (26.3 - 25) / (3 / √20) = 1.836

Next, we need to find the probability of Z > 1.836 using a Z-table or a Z-score calculator. The probability can be found in the right-tail of the Z-distribution.

For part (b), we can directly use the Z-score formula again to find the probability that a child ages 2-5 watches over 26.3 hours of TV per week. The Z-value will be the same as before, 1.836. The probability can be found in the right-tail of the Z-distribution.