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