Please review my homework

Check for errors and especially make sure that the formulas are correct ( thank you)

A Cub Scout pack has 12 children in it. In how many different ways could the pack leader select 3 Cub Scouts to attend a summer camp?

Answer

12C3ways =12! /3 ! 9!=(12 *11 *10)/3 * 2 *1)

1320/6 =220 ways

16 students participated in the tournament. In how many ways can they get first, second and third place?

Answer

16 ways to win first place

15 ways to win second place

14 ways to win third place

Therefore The number of ways is 16 * 15 * 14 =3360 ways

According to a recent survey, approximately 68% of students at this campus are women. A group of 20 students are randomly selected. What is the probability that 15 of them are women?

Answer

X~Binomial

n=20, p=0.68

P(X=x)=xC20*(0.68^x)*( 0.32^(20-x)

the probability is

P(X=15)= 0.1598922

0.1598922 round 2 decimal place= 0.16

the probability is 0.16

A sample of 200 smokers was asked at what age they started smoking. The sample mean was 18.3 years with a standard deviation of 4.35 years. Construct a 95% confidence interval for the mean age that all smokers begin smoking.

Answer

n = 200

sample mean = 18.3

s = 4.35

Z for 95% confidence interval = Z_0.025= 1.96

S (X + Zo.025 * 4.35 18.3 + 1.96 * 200 18.3 # 0.603937.6 - 850 191.3/