Asked Jan 17, 2020

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.

Births of Boys With n = 20 births and p = 0.512 for a boy, find P(fewer than 8 boys).


Expert Answer

Step 1

The probability for the birth of a boy p  = 0.512.

The improbability for the birth of a boy q  = 0.488 (1–0.488).

The number of births n is 20.

Requirement check:

Condition 1:np≥5

Condition 2: nq≥5

Step 2

Condition 1: np≥5

Substitute 20 for n and 0.512 for p in the np.

Statistics homework question answer, step 2, image 1
Step 3

Thus, the given requirement of  is satisfied.

Condition 2: nq≥5


Statistics homework question answer, step 3, image 1

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