Question

Using Normal Approximation. In Exercises 5–8, do the following: If the requirements of $np⩾5$ and$nq⩾5$ are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if $np<5$or $nq<5$, 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

The method of normal approximation should not be used.

Step-by-step solution

 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.

Check the requirement necessary for normal approximation

It is required that$np⩾5$ and $nq⩾5$.

The values are computed below:

$$\begin{gathered} np=\left(20\right)\left(0.2\right) \\ =4 \\ <5 \end{gathered}$$

$$\begin{gathered} nq=\left(20\right)\left(1-0.2\right) \\ =16 \\ <5 \end{gathered}$$

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