Sampling Distributions - How to Solve

Suppose x has the b(20 0.5) distribution. what is the mean of x? How would you find SD? What about proportion, or p-hat? Variance?

Binomial distributions have B(N, P). To find the mean, you multiply n * p. For SD you’d do sqrt(n*p(1 - p). Proportions: p-hat = X/N. Variance for this quantity is sqrt(P(1-p)/n

The weights of oranges is Normally distributed with mean 14 and SD 2. What is sampling distribution of the sample mean of 10 oranges?

14 is also the mean. For SD, do 2 divided by sqrt(10)

Hotel rooms have mean cost 131.8 and SD 29.12. What is probability mean of 15 hotels will be 150?

Remember to find new SD - 29.12/sqrt(15). Then use probability calculator.

We have a Normal distribution with mean 8.1 and SD .1. If we increase sample size by 2, by what factor would SD change?

1/sqrt(2). This because the SD doesn’t change - so it is multiplied by 1. But the N does change by 2 times, as indicated by the 2 here.

A poll of 600 men find 85% support their wives. If take that same statistic to 1200 men, what is the amount of men that support their wives?

Do .85 times 1200.

We have a Normal distribution with mean 250 and SD 6. If we want the SD of the sampling distribution to be 1, what sample size do we need.

Multiply 6 times 1, then square the result to get the sample size N.