Statistics and Probability Answers

1. A sample with a size n=3 is drawn from a set of 5,6,812, and 20. Construct the sampling distribution of the medians.

2. Random samples with size 4 are drawn from the population containing the values 14, 19, 26, 31, 48, 53.

a. Construct a sampling distribution of the sample means.

b. Find the mean of the sample means.

c. Compute the standard error of the sample means.

1.    Stephen has found out that the average weight of packed gummy candies selected from a normally distributed population is 200g with a standard deviation of 8g. Find the point and the interval estimates of all gummy candies, using a 95% confidence level.

N value is 25

2.    In an interview held among 18 randomly selected elementary teachers of a certain school, the mean salary was found to be Php21000 with a standard deviation of Php3000. Use 95% confidence to estimate the population mean where the sample came from.

The lifespan of rats raised in a laboratory is approximately normally distributed with a standard

deviation of 5.9 months. A sample of 31 rats reared to adulthood in a laboratory have a mean life span

of 27.3 months.

a) Find a 95 % confidence interval for the population mean of all rats raised in a laboratory.

b) What can we assert with 95% confidence about the possible size of our error if we estimate the

mean lifespan of all laboratory rats to be 27.3 months?

c) How large a sample is needed if we wish to be 95% confident that our sample mean will be within

3.5 months of the true mean?