Problem 7BSC

Finding μ, σ, and Unusual Values. In Exercises, 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 standard deviation σ . Also, use the range ruh of thumb to find the minimum usual value μ – 2σ and the maximum usual value μ – 2 σ.

Identity Theft In a Gallup poll of 1013 randomly selected adults, 66% said that they worry about identity theft, so n = 1013 and p = 0.66.

Answer:

Step 1 of 1

Given, n = 1013 and p = 0.66, q = 1 - p = 0.34

Binomial distribution with n trials and the probability of success for one trial is p.

Using the given values of n and p to find the mean μ and standard deviation σ

Mean μ = np = 10130.66 = 668.58

Standard deviation σ = = = 15.077

Using the range rule of thumb to find the minimum usual value μ – 2σ and the maximum usual value μ – 2σ.

We find the minimum and maximum usual values according to the equations you gave

minimum: mean - 2(standard deviation)

= 668.58 - 2(15.077)

= 638.426

maximum: mean + 2(standard deviation)

= 668.58 + 2(15.077)

= 698.734