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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鈮�15)=PZ鈮�15-100(0.11)100(0.11)(1-0.11)=P(Z鈮�1.28)=1-0.8997=0.1003

Thus, the resultant probability is 0.1003.

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Most popular questions from this chapter

Lefties A total of 11%of students at a large high school are left-handed. A statistics teacher selects a random sample of 100 students and records L= the number of left-handed students in the sample.

a. Explain why L can be modeled by a binomial distribution even though the sample was selected without replacement.

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

Ana is a dedicated Skee Ball player who always rolls for the 50-point slot.

Ana鈥檚 score Xon a randomly selected roll of the ball has the probability distribution

shown here with mean 渭X=23.8and standard deviation 蟽X=12.63.

A player receives one ticket from the game for every 10points scored. Define T=number of tickets Ana gets on a randomly selected roll.

a. What shape does the probability distribution of Thave?

b. Find the mean of T.

c. Calculate the standard deviation ofT.

Each entry in a table of random digits like Table Dhas probability $$ of being a 0 , and the digits are independent of one another. Each line of Table D contains 40 random

digits. The mean and standard deviation of the number of 0 s in a randomly selected line will be approximately

a. mean =0.1, standard deviation =0.05.

b. mean =0.1, standard deviation =0.1.

c. mean =4, standard deviation =0.05.

d. mean =4, standard deviation =1.90.

e. mean =4, standard deviation =3.60.

Baby elk Refer to Exercise 77 . How surprising would it be for more than 4 elk in the sample to survive to adulthood? Calculate an appropriate probability to support your answer.

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p ?

a. n=10,p=0.5

b. n=40,p=0.88

c. n=100,p=0.2

d. n=100,p=0.99

e.n=1000,p=0.003
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