Question

A. C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages of 2 and 5 are randomly selected, find . Give answer to three decimal places.

Answer 1

The following information about the mean and standard deviation has been provided:

μ=25, σ=3, n=20

We need to compute Pr(Xˉ≥26.3).

The corresponding z-value needed to be computed is:

$Z = \frac{\bar X-\mu}{\sigma/\sqrt{n}} = \frac{ 26.3-25}{ 3/\sqrt{ 20}} = 1.9379$

Therefore, we get that

$\Pr(\bar X \geq 26.3) = \Pr\left(Z \ge \frac{ 26.3-25}{ 3/\sqrt{ 20}}\right) = \Pr(Z \ge 1.9379)$

==l-0.9737 -0.026

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