Question

Lefties Refer to Exercise 99.

a. Justify why L can be approximated by a Normal distribution.

b. Use a Normal distribution to estimate the probability that 15 or more students in the sample are left-handed.

Short answer

1. The $L$is about regularly distributed.
2. The resultant probability is$0.1003.$

Step-by-step solution

Part (a) Step 1: Given information

The number of students$\left(n\right)=100$

Left-handed students as a percentage of total students$\left(p\right)=0.11$

Part (a) Step 2: Calculation

Consider,

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

Therefore, the L is about regularly distributed.

Part (b) Step 1: Given information

The number of students $\left(n\right)=100$

Left-handed students as a percentage of total students$\left(p\right)=0.11$

Part (b) Step 2: Calculation

If 15 or more pupils are left-handed, the probability is calculated as"

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

Thus, the resultant probability is 0.1003.