Would you favor a law requiring a police permit to buy a gun? 73% of american me

Question

Would you favor a law requiring a police permit to buy a gun? 73% of american men and 86% of american women would favor such a law.

a) A candidate for city council is speaking to a breakfast group of 38 men. The topic of gun permits came up. What is the probabliity that the majority of the audience (at least two thirds) will support gun permits? Assume the group is representative of all us men.

b) Answer part (a) if our candidate is speaking to a women's group with 45 women in the audience. Assume the group is representative of all us women.

c) Is the normal approximation to the proportion P hat=r/n valid in both applications, explain?

Explanation / Answer

a) we want the probability that more than (2/3) of 38 men, in other words 26 or more, favor the law, given that 73% of all men favor it: 1-binomcdf(38,0.73,25) = 0.7961 b) here 2/3 of 45 is 30, so we want probability of 30 or more women who favor out of 45, given that 86% of all women favor: 1-binomcdf(45,0.86,29) = 0.9998 c) in part a), np = 38*0.73 > 10 and nq = 38*0.27 > 10, so yes in part b), np = 45*0.86 > 10 but nq = 45*0.14 < 10, so no

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