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Chapter 5: Q. 5.28 (page 176)

Twelve percent of the population is left handed. Approximate the probability that there are at least 20 lefthanders in a school of 200 students. State your assumptions.

Short Answer

Expert verified

The probability that there are at least20lefthanders in a school of 200 is0.8365.

Step by step solution

01

Step 1. Given Information.

Twelve percent of the population is left handed.

So, P (left handed)=0.12

02

Step 2. Assumption

Assuming that except12%of the population all others are right handed.

03

Step 3. Approximate binomial distribution with normal distribution. 

P (left handed) =0.12

渭=200脳0.12=24

蟽=np(1-p)

Where, n=200and p=0.12

蟽=(200脳0.12)(1-0.12)蟽=24脳0.88蟽=21.12蟽鈮�4.60

P(X鈮�19.5)=PZ鈮�19.5-244.60=PZ鈮�-0.98=1-1-蠁0.98=0.8365

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