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StatisticsQ&A LibraryUsing 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).Question

Asked Jan 17, 2020

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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).

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*.

Step 3

Thus, the given requirement of is satisfied.

Condition 2: *nq≥5*

Substitute...

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