Question

1. If 12% of a population has green eyes what is the probability that out of a sample of 586 at least 80 will have green eyes? what would be the mean and standard deviation for the sample?

2. If SAT test scores are normally distributed with a mean of 1600 and a standard deviation of 75

a. what is the mean and standard deviation for non-standard normal distribution of this data

b. what is the mean and standard deviation for the standard normal distribution?

3. Assume that cans of coke are filled so that the amounts are normally distributed with a mean of 12 oz and a standard deviation of 1.1 oz

a. find the probability that a single can of coke has less than 11.9 ounces

b. find the probability that in a sample of 25 cans of coke their average will be less than 11.9 ounces

Answer 1

Solution1:

mean=np=586*0.12=70.32

standard deviation =sqrt(n*p*q)=sqrt586*0.12*(1-0.12)=7.866

Solution2:

a. what is the mean and standard deviation for non-standard normal distribution of this data

mean=1600

standard deviation =75

b. what is the mean and standard deviation for the standard normal distribution

mean=0

standard deviation=1

Solution3:a)

n=1

mean=12

sd=1.1

P(xbar<11.9)

use below r code to get area under z

pnormGC(bound=11.9,region="below",mean=12,sd=1.1,graph=TRUE)

0.4637824

0.4638

Soution3b:

mean=12

sd=sigma/sqrt(n)=1.1/sqrt(25)

=1.1/5

= 0.22

pnormGC(bound=11.9,region="below",mean=12,sd= 0.22,graph=TRUE)

=0.3247181

0.3247