## Distribution of sample means Exercise

1. The results of an examination held one year have a mean μ, of 53 and a standard deviation, σ, of 12.5. If random samples of size 10 are taken from schools, find

a. The mean of the sample means

b. The standard deviation of the sample means.

2. The students from a school all do an arithmetic test. The mean mark is 34 out of 40 and the standard deviation is 6.2. If samples of size 20 are taken from the school, find:

a. The expected value of the sample means

b. The variance of the sample means.

3. Complete the table

 Population mean Population standard deviation sample size Mean of sample means Variance of sample means Standard deviation of sample means Question (μ) (σ) (n)   a 85 12 100 b 30 5 1.25 c 25 5.6 1.2 d 23 50 3 e 400 230 12

4. A population has a normal distribution with a mean of 20 and a variance of 9.

a. Find the standard deviation of the population.

b. Find the mean and variance of the distribution of samples of size 100 taken from this population.

5. To find the mean life and standard deviation of a type of light bulb a large number of samples of 100 bulbs are tested. The mean of the distribution of the sample mean was found to be 2000 hours and standard deviation was 110 hours. Find the mean life and standard deviation of the population of these light bulbs.

6. The number of cars owned by each family on an island is 2.5 with a variance of 0.9. A statistician wants to take samples so that the standard deviation of the sample means is 0.06. How many families should she include in her sample?