Chapter 6.3, Problem 103E

a.

To determine

To explain: The reason of L being normally distributed.

Explanation of Solution

Given:

Number of students (n) = 100

Proportion of students that are left-handed (p) = 0.11

Calculation:

Here,

  $\begin{array}{l}np=100\left(0.11\right)=11>10\\ n\left(1-p\right)=100\left(1-0.11\right)=89>10\end{array}$

Hence, the L is approximately normally distributed.

b.

To determine

To find: The probability that 15 or more students are left-handed.

Explanation of Solution

The probability that 15 or more students are left-handed is calculated as”

  $\begin{array}{c}P\left(X\ge 15\right)=P\left(Z\ge \frac{15-100\left(0.11\right)}{\sqrt{100\left(0.11\right)\left(1-0.11\right)}}\right)\\ =P\left(Z\ge 1.28\right)\\ =1-0.8997\\ =0.1003\end{array}$

Thus, the required probability is 0.1003.