## A recent study indicated that 20% of adults exercise... Find

Standard deviation, mean, variance, z-scores, t-tests, etc.
FWT
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Joined: Sat Feb 28, 2009 8:53 pm

### A recent study indicated that 20% of adults exercise... Find

A recent study indicated that twenty percent of adults exercise regularly. Suppose that five adults are selected at random. Use the binomial probability formula to find the probability that the number of people in the sample who exercise is:

a. exactly 3
b. at least 3

Also, find the:

c. mean
d. standard deviation

stapel_eliz
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FWT wrote:A recent study indicated that twenty percent of adults exercise regularly. Suppose that five adults are selected at random. Use the binomial probability formula to find the probability that the number of people in the sample who exercise is:

a. exactly 3
b. at least 3

The formula for the probability P that x of n results will be "good" is:

. . . . .$P(x)\, =\, C(n,\, x)\,p^x\, (1\, -\, p)^{n\, -\, x}$

In this case, n = 5 and p = 0.2. Then:

. . . . .$\mbox{a. }\, P(3)\, =\, \frac{5!}{2!3!}\, (0.2)^3\, (0.8)^2$

Evaluate to find the needed value.

For part (b), note that "at least three" means three, four, or five. Compute all three, and sum the values.

FWT wrote:Also, find the:

c. mean
d. standard deviation

The expected value (or mean) is np, or (5)(0.2). The standard deviation is given by:

. . . . .$\sigma\, =\, \sqrt{np(1\, -\, p)}$