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Chapter 6: Q. 103 (page 430)

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

Expert verified
  1. The Lis about regularly distributed.
  2. The resultant probability is0.1003.

Step by step solution

01

Part (a) Step 1: Given information

The number of students(n)=100

Left-handed students as a percentage of total students(p)=0.11

02

Part (a) Step 2: Calculation

Consider,

np=100(0.11)=11>10n(1-p)=100(1-0.11)=89>10

Therefore, the L is about regularly distributed.

03

Part (b) Step 1: Given information

The number of students (n)=100

Left-handed students as a percentage of total students(p)=0.11

04

Part (b) Step 2: Calculation

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

P(X≥15)=PZ≥15-100(0.11)100(0.11)(1-0.11)=P(Z≥1.28)=1-0.8997=0.1003

Thus, the resultant probability is 0.1003.

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