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Chapter 6: Q7 (page 226)

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

Guessing on Standard TestsWith guesses and for a correct answer, findP(at least 6 correct answers).

Short Answer

Expert verified

The method of normal approximation should not be used.

Step by step solution

01

 Step 1: Given information

A sample of 20 guesses of answers on a test is considered. The probability of a correct answer is equal to 0.2.

02

Check the requirement necessary for normal approximation

It is required thatnp⩾5 and nq⩾5.

The values are computed below:

np=200.2=4<5

nq=201-0.2=16<5

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

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