Unit 5: Sampling Distributions

The Central Limit Theorem states that:

The standard deviation of the sampling distribution of [math] is:

As the sample size [math] increases, the sampling distribution of [math]:

For the sampling distribution of [math] to be approximately normal, we need:

The mean of the sampling distribution of [math] is:

Increasing the sample size will:

The 10% condition for sampling distributions states that:

If a population has mean [math] and standard deviation [math], the standard error of [math] for samples of size [math] is:

A statistic is said to have high variability but low bias. This means:

If [math] based on a sample of [math], the standard deviation of the sampling distribution of [math] is approximately:

A random variable X has the following distribution: P(X=1) = 0.2, P(X=2) = 0.5, P(X=3) = 0.3. What is E(X)?

If X and Y are independent random variables with Var(X) = 4 and Var(Y) = 9, what is Var(X + Y)?

If E(X) = 10 and SD(X) = 3, and Y = 2X + 5, what are E(Y) and SD(Y)?

If X has mean 20 and Y has mean 30, what is the mean of X + Y?

Which of the following is a continuous random variable?

For a continuous random variable, P(X = 5) equals:

If Var(X) = 25, what is SD(X)?

What are the mean and standard deviation of the sampling distribution of p̂?

What is the probability that the sample mean exceeds 510?

Which condition is NOT met for using the normal approximation to the sampling distribution of x̄?

As the sample size increases from 25 to 100, what happens to the standard deviation of the sampling distribution of x̄?

A bottling company fills bottles with a mean of 500 mL and standard deviation of 5 mL. A quality inspector takes a random sample of 25 bottles and measures the mean. What is the probability that the sample mean is less than 498 mL?

In a large population, 35% of voters support a ballot measure. A polling firm takes a random sample of 400 voters. What is the approximate probability that the sample proportion exceeds 0.40?

A population has mean μ = 100 and standard deviation σ = 16. For random samples of size n = 64, what is the probability that the sample mean x̄ exceeds 104?