Question

The mean systolic blood pressure of adults is 120 millimeters of mercury (mm Hg) with a standard deviation of 5.6. Assume the variable is normally distributed.

1) If an individual is randomly selected, what is the probability that the individual's systolic pressure will be between 120 and 121.8 mm Hg.

2) If a sample of 30 adults are randomly selected, what is the probability that the sample mean systolic pressure will be between 120 and 121.8 mm Hg.

-Central Limit Theorem -

please solve the following problem and explain how you approached each step (include how you solved the problem with the calculator):

Answer 1

Given and .

For P(x1<X<x2), use TI-83 function normalcdf(x1, x2, mean, sd).

1) For individual, use and .

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2) The Central limit theorem states that the sampling distribution of the sample mean is approximately normally distributed with mean μ and standard deviation σ/√n if either n is large or population is normal.   

For sample mean, use and .

No need to solve this. In calculator, you can enter this expression directly.