Sampling Distribution Mean

The distribution of heights for 16-year-old females is approximately Normal with population mean 64 inches and standard deviation 2.5 inches. A physician takes a random sample of 20 16-year-old females. What is the MEAN height of the sampling distribution of the sample mean? Round to two decimal places. DON'T FORGET UNITS!

The distribution of heights for 16-year-old females is approximately Normal with population mean 64 inches and standard deviation 2.5 inches. A physician takes a random sample of 20 16-year-old females. What is the STANDARD DEVIATION height of the sampling distribution of the sample mean? Round to two decimal places. DON'T FORGET UNITS!

At Chipotle, the distribution of sodium content is approximately Normal with population mean 2000 mg and standard deviation 500 mg. Suppose Mrs. Hackett wants to take a bunch of random samples to investigate this. For which of the following sampling distributions would she get a MEAN closest to the TRUE POPULATION MEAN?

• Samples of size 100

• Samples of size 50

• Samples of size 25

• All of these sample sizes

At Chipotle, the distribution of sodium content is approximately Normal with population mean 2000 mg and standard deviation 500 mg. Suppose Mrs. Hackett wants to take a bunch of random samples to investigate this. For which of the following sampling distributions would she get the SMALLEST standard deviation?

• Samples of size 100

• Samples of size 50

• Samples of size 25

• All of these sample sizes

What does this mean: E(X ̅ )=E(X)=μ

• This is called the expected standard deviation. When the sample SD is the population SD

• This is called the expected sample mean where the sample mean equals the sample mean.

• This is called the expected value. When the sample mean will equal the population mean.

How do you find the probability that a sample mean will be less than 70, P(x ̅ < 70).

You already know the standard error, E(X ̅ )=E(X)=μ and it is normally distributed.

What do you do next?

• this is the expected value

• find 70 in the z-table

• 

Which of the following is true in regards to the Central Limit Theorem?

• Assume a normal distribution when n>=30

• Assume a normal distribution when n>=20

• Assume a normal distribution when n>=50

• Assume a normal distribution when n>=100

If a problem states: A random sample is drawn from a population mean of 90 , standard deviation of 5, with n = 20. what is the probability the sample mean is less than 80.

Can you conclude that the sampling distribution of the sample mean is normally distributed?

• Yes

• No

Suppose the average time to complete a final exam is 65 minutes with a standard deviation of 7.5 minutes.  Suppose you take a random sample of 100 students, select ALL statements that are true.

• The mean of the sampling distribution is 65 minutes.

• The standard error is 0.75 minutes.

• The shape of the sampling distribution is approximately normal because the sample size is large.

• None are true.

Suppose the time that U.S. workers remain unemployed is normally distributed with a mean of 20.9 weeks before finding their next job and a population standard deviation of 6.0 weeks. If you take a random sample of 50 U.S. workers who were unemployed six months earlier and ask them to report the duration of their unemployment, what is the probability that the average time spent unemployed was more than 23 weeks? (Note: do not round your calculations until the last step)

• 0.2456

• 0.1271

• 0.0918

• 0.0068