1. The IQ (intelligence quotient) of the people of a country is normally distributed with a mean of 100 and a standard deviation of 16.

Find the probability that a random sample of 45 people from that country has a mean IQ of less than 97.

2. A sample of the heights of 100 school soccer players is taken from a population of Victorian schools with a mean of 156 cm and a variance of 625.

Find the probability that the sample mean will be within 4 cm of the population mean.

3. The standard deviation of the weights of objects in a large population is 4.66 kg.

If random samples of size 90 are drawn from the population, find the probability that a sample mean will differ from the true population mean by less than 0.7 kg.

4. A random sample of size 200 is taken from a binomial distribution with n =25 and p = 0.4.

Find the probability that the sample mean is greater than 10.4.

5. A random sample of size 40 is taken from a Poisson distribution with λ = 5.

Find P(< 5.4)

6. To find the mean life and standard deviation of a make of light bulbs a large number of samples of size 50 are taken. The mean of the resulting distribution of sample means is 2000 hours and the standard deviation is 250 hours. Find the mean and standard deviation of the light bulbs (to nearest hour).

7. The mean price of Toyobishi cars is $31,000 with a standard deviation of $4, 500. If a random sample of 35 cars is taken, what is the probability that the mean of the sample of Toyobishi cars will be more than $32,000?

8. A large number of samples of size 40 is taken with replacement from the following distribution.

x
1
2
3
4
5
6
f
9
18
22
25
18
8

a. Find the mean and standard deviation of the distribution above.

b. Find the mean and standard deviation of the sample mean

c. Find the probability that a sample mean will exceed 3.