Suppose a simple random sample of size nequals36 is obtained from a population with mu equals 74 and sigma equals 6. (a) Describe the sampling distribution of x overbar. (b) What is Upper P (x overbar greater than 75.9 )? (c) What is Upper P (x overbar less than or equals 71.95 )? (d) What is Upper P (73 less than x overbar less than 75.75 )?

Part a)

The simple random sample of size n=36 is obtained from a population with

and

The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.

Therefore the sampling distribution has a mean of

The standard error of the means becomes the standard deviation of the sampling distribution.

Part b) We want to find

We need to convert to z-score.

Part c)

We want to find

We convert to z-score and use the normal distribution table to find the corresponding area.

Part d)

We want to find :

We convert to z-scores and again use the standard normal distribution table.

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)