C: A recent survey found that 40% of all adults wear glasses for driving. In a r

Question

C: A recent survey found that 40% of all adults wear glasses for driving. In a random sample of 20 adults, 1. What is the probability that 5 adults wear glasses for driving? (by formula and table) 2. What is the probability that at most 10 adults wear glasses for driving? 3. What is the probability that at least 8 adults wear glasses for driving? 4. What is the probability that less than 12 adults wear glasses for driving? 5. W 6. What is the variance of the number who wear glasses? hat is the expected number of adults who wear glasses for 20 people? hat is the standard deviation of the number who wear glasses?

Explanation / Answer

p = 0.4

n = 20

P(X =x) = 20Cx * 0.4x * (1-0.4)20-x

1) P(X = 5) = 20C5 * 0.45 * 0.615 = 0.0746

2) P(X < 10) = P(X = 0) + P(X = 1) +... + P(X = 10)

= 0.8725

3) P(X > 8) = P(X = 8) + P(X = 9) +... + P(X = 20)

= 0.5841

4) P(X < 12) = P(X = 0) + P(X = 1) +... + P(X = 11)

= 0.9435

5) expected value = n * p = 20 * 0.4 = 8

6) Variance = n * p *(1-p) = 20 * 0.4 * 0.6 = 4.8

7) standard deviation = sqrt(4.8) = 2.2

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