Hi please review my homework to make sure I answered them correctly and help with question 3( thank you)

1)A campus club has 16 members.In how many ways can they elect a president, a vice-president, and a secretary?

Answer

According to the fundamental counting principlewe have to multiple all the events together

16 15 14 = 3360

2)According to the 1998 Health and Human Service's National Household Survey on Drug Abuse, 18% of children between the ages of 12 and 17 are cigarette smokers.If 8 children in this age group are selected randomly find the probability that 2 of them are cigarette smokers.You may assume this is a binomial probability.

Answer

X represents the number of age group smokers = 8

X~ binomial =8,0.18

The required probability is

P(X=2) =8C2 x (0.18)2x(0.82)6

=28 x 0.0324 x 0.304

P(X=2)= 0.2758

3 The mean systolic blood pressure of young female adults is approximately normally distributed with a mean of 125 and a standard deviation of 24.A random sample of 100 young female adults is taken.Find the probability that the mean of the sample is greater than 127.

Help with this one

4.Sixty-four college students took a placement exam.Their mean score was 29.5 points with a standard deviation of 7.3 points.Construct a 95% confidence interval for the mean score on this placement exam for all students.

Answer