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Chapter 6: Q6 (page 289)

Using Normal Approximation. In Exercises 5鈥�8, do the following: If the requirements of np猢�5andnq猢�5are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; ifnp<5or nq<5, then state that the normal approximation should not be used.

Births of BoysWithbirths and p= 0.512 for a boy, find P(Exactly 5 boys)

Short Answer

Expert verified

The normal approximation method cannot be used as np<5and nq<5.

Step by step solution

01

Given information

A sample of 8 births is considered. The proportion of boys (p) is equal to 0.512.

02

Check the requirement necessary for normal approximation

It is required that np猢�5andnq猢�5 .

The values are computed below:

np=80.512=4.10<5

nq=81-0.512=3.90<5

As the requirement is not fulfilled, the normal approximation cannot be applied to compute the probability value.

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