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 least $20$ lefthanders in a school of 200 is $0.8365$ .

Step by step solution

Step 1. Given Information.

Twelve percent of the population is left handed.

So, P (left handed) $= 0.12$

Step 2. Assumption

Assuming that except $12 %$ of the population all others are right handed.

Step 3. Approximate binomial distribution with normal distribution.

P (left handed) $= 0.12$

$μ = 200 \times 0.12 = 24$

$σ = \sqrt{n p (1 - p)}$

Where, $n = 200$ and $p = 0.12$

$σ = \sqrt{(200 \times 0.12) (1 - 0.12)} σ = \sqrt{24 \times 0.88} σ = \sqrt{21.12} σ \approx 4.60$

$P (X \geq 19.5) = P (Z \geq \frac{19.5 - 24}{4.60}) = P (Z \geq - 0.98) = 1 - \{1 - φ (0.98)\} = 0.8365$

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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

Step by step solution

Step 1. Given Information.

Step 2. Assumption

Step 3. Approximate binomial distribution with normal distribution.

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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

Step by step solution

Step 1. Given Information.

Step 2. Assumption

Step 3. Approximate binomial distribution with normal distribution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Geometry

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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.