One day, 900 men and 900 women enter a shop. Each person decides to buy (or...
One day, 900 men and 900 women enter a shop. Each person decides to buy (or not) an advertised box of chocolates, which is on sale, with probability 1 2 . What is the (approximate) probability that the number of women who make this purchase will not differ from the number of men who buy the box by more than 50?
Homework Answers
p1 - proportion of men who make this purchase
p2- proportion of women who make this purchase
P( |p1^- p2^| < 50/900)
Z = ((p1^- p2^) - (p1 - p2))/sqrt(p1*q1/n1 + p2*q2/n2)
here p1 = q1 = p2 = q2 = 0.5
n1 = n2 = 900
hence
Z = (p1^- p2^) /sqrt(0.5*0.5/900 + 0.5*0.5/900)
=(p1^- p2^)/ 0.023570
P( |p1^- p2^| < 50/900)
= P(|Z| < 50/900/0.023570 )
= P(|Z| < 2.35704 )
=
P (−2.35704<Z<2.35704 )=0.9818
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