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.

Clinical Trial In a clinical trial of the cholesterol drug Lipitor, 94 subjects were treated with 80 mg of Lipitor, and 6.4% of them developed headaches, so n = 94 and p = 0.064.

Answer:

Step 1 of 1

Given, n = 94 and p = 0.064, q = 1 - p = 0.936

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 = 940.064 = 6.016

Standard deviation σ = = = 2.3729

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)

= 6.016 - 2(2.3729)

= 1.2702

maximum: mean + 2(standard deviation)

= 6.016 - 2(2.3729)

= 10.7618