Chapter 11.5, Problem 2GP

(a)

To determine

To find: The number of members have between $26\text{and}50$ friends.

Answer to Problem 2GP

The range is $5.6<X<10.8$ .

Explanation of Solution

Given:

The normal distribution has a mean of $38$ and a standard deviation of $12$ .

Calculation:

  $26\text{and}50$ are $\sigma$ away from the mean.

Therefore, about $68\%$ of the data are between $26\text{and}50$ .

Since,

  $\begin{array}{c}820\times 68\%=820\times \frac{68}{100}\\ =558\end{array}$

Therefore $558$ of the members have between $26\text{and}50$ friends.

(b)

To determine

To find: The probability that a random member will have more than $14$ friends.

Answer to Problem 2GP

The probability is $95.15\%$ .

Explanation of Solution

The values greater than $14$ are more than $\mu -2\sigma$ .

  $95\%$ of the data are between $\mu -2\sigma \text{and}\mu +2\sigma$ .

  $0.15\%$ are greater than $3\sigma$ .

Therefore the probability is calculated as:

  $\begin{array}{c}\text{Probability}=95\%+0.15\%\\ =95.15\%\end{array}$

The probability is $95.15\%$ .