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Chapter 6: Q.105 (page 406)

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

Short Answer

Expert verified

Because the required requirements are only met in option(c), option(c) is the correct response. n=100,p=0.2

Step by step solution

01

Given information 

Given in the question that, 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

02

Explanation

The following conditions must be met in order to approximate a binomial distribution using a normal distribution:

np鈮�10

nq鈮�10

(a) np=10(0.5)=5, nq=n(1-p)=10(1-0.5)=5

(b) localid="1649527995119" np=40(0.88)=35.2,nq=n(1-p)=40(1-0.88)=4.8

(c) np=100(0.2)=20,nq=n(1-p)=100(1-0.2)=80

(d) np=100(0.99)=99,nq=n(1-p)=100(1-0.99)=1

(e)np=1000(0.03)=3,nq=n(1-p)=1000(1-0.003)=997

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