1. In a private school the probability of a student being a girl is 58%? Show al
ID: 3176178 • Letter: 1
Question
1. In a private school the probability of a student being a girl is 58%? Show all work. A) What is the probability of obtaining 2 girls in a random sample of 8 kids? B) What is the probability of obtaining 2 girls or less in a random sample of 8 kids? C) What is the probability of at least 3 girls in a random sample of 8 kids? D) What is the expected amount of girls you would obtain in a random sample of 8 kids? E) What is the standard deviation of girls you would obtain in random sample of 8 kids? F) Is it unusual to have 2 girls in a random sample of 8 kids? 7 girls? G) What type of distribution is described in the preceding questions?
Explanation / Answer
p = 0.58
n = 8
P(X = x) = 8Cx * 0.58x * (1 - 0.58)8-x
a) P(X = 2) = 8C2 * 0.582 * 0.426
= 0.0517
b) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 8C0 * 0.580 * 0.428 + 8C1 * 0.581 * 0.427 + 8C2 * 0.582 * 0.426
= 0.0634
c) P(X > 3) = 1 - P(X < 2)
= 1 - 0.0634
= 0.9366
d) E(X) = n * p = 8 * 0.58 = 4.64 or 5 (approx)
e) standard deviatio = sqrt(n * p * (1 - p))
= sqrt(8 * 0.58 * 0.42)
= 1.4 or 1 (approx.)
f) P(X = 2) = 8C2 * 0.582 * 0.426 = 0.0517
Since, the probability is not less than 0.05, this is not unusual.
g) type of distribution is binomial distribution
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