# statistics, probabilities, binomials

Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean μ and the standard deviation σ. Also, use the range rule of thumb to find the minimum usual value μ – 2σ and the maximum usual value μ + 2σ.

N = 60, p = 0.7

μ =

(Round to one decimal place as needed.)

σ =

μ – 2σ

μ + 2σ

**2) ** A candy company claims that 17% of its plain candies are orange, and a sample of 200 such candies is randomly selected.

**a.) ** Find the mean and standard deviation for the number of orange candies in such groups of 200.

μ =

(Round to one decimal place as needed.)

σ =

**b.) **A random sample of 200 candies contains 15 orange candies. Is this result unusual? Does it seem that the claimed rate of17% is wrong?

**3)**** a.) ** For classes of 169 students, find the mean and standard deviation for the number born on the 4th of July. Ignore leap years.

**b.) ** For a class of 169 students, would two be an unusually high number who were born on the 4th of July?

a) (Round to six decimal

places as needed.)

The value of the mean is μ =

The value of the standard deviation is σ =

**b.** Would 2 be an unusually high number of individuals who were born on the

4th of July?

Why? Is 2 the minimum or is it greater?