Question

7. The random variable X is distributed normally with a mean of 12.46 and variance of 13.11. You collect a random sample of size 37.
a. What is the probability that your sample mean is between 12 and 13?
b. What is the probability that a single observation is between 12 and 13?
c. What is the probability that all of your observations are between 12 and 13?
a. Z = (score-mean)/SEm

SEm = SD/√n

SD = √variance

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

b. Z = (score-mean)/SD

Use same table.

c. I'm not sure about this one.

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