PLEASE EXPLAIN! According to a survey, 40% of women between the ages of 25 and 2

ID: 3050126 • Letter: P

Question

PLEASE EXPLAIN!

According to a survey, 40% of women between the ages of 25 and 29 have never been married. In a group of 10 women in this age group,

what is the chance that two or fewer were never married?

what is the probability of having at least one woman who never married?

what is the chance of having 6 women who have been married?

would it finding only one woman who had never been married be unusually low?

What is the mean number of women who have never been married in groups of 60 women in this age group?

What is the variance in groups of 75 women?

p = 0.4

n = 10

a) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 10C0 * 0.40 * 0.610 + 10C1 * 0.41 * 0.69 + 10C2 * 0.42 * 0.68

= 0.1673

b) P(X > 1) = 1 - P(X = 0)

= 1 - 10C0 * 0.40 * 0.610

= 1 - 0.006

= 0.994

c) P(X = 6) = 10C6 * 0.46 * 0.64 = 0.1115

d) n = 60

Mean = n * p = 60 * 0.4 = 24

e) n = 75

Variance = n * p * (1 - p) = 75 * 0.4 * (1 - 0.4) = 18

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