Question

During a severe storm, electrical transformers that function independently are expected to operate 85 percent of the time. Suppose 20 electrical transformers are randomly selected from the population. Let the random variable
T represent the number of electrical transformers operating during a severe storm. Which of the following is the best interpretation of the random variable T ?

A.It is a binomial variable with mean 17 transformers and standard deviation \sqrt{2.55}2.55 transformers.
B. It is a binomial variable with mean 17 severe storms and standard deviation \sqrt{2.55}2.55 severe storms.
C. It is a binomial variable with mean 0.85 transformer and standard deviation 20 transformers.
D. It is a variable that is not binomial with mean 17 transformers and standard deviation \sqrt{2.55}2.55transformers.
E. It is a variable that is not binomial with mean 0.85 severe storm and standard deviation 20 severe storms.

Answer 1

Answer:

A.It is a binomial variable with mean 17 transformers and standard deviation $\sqrt{2.55}$ transformers.

Explanation:

Since the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random. Assuming the variable is a binomial variable. We have:

Mean = number of samples * probability

Standard Deviation = $\sqrt{mean*(1-probability)}$

mean = 85% * 20 = 0.85*20 = 17 transformers

Standard deviation = $\sqrt{mean*(1-0.85)}=\sqrt{17*0.15} =\sqrt{2.55}$ transformers.

Thus, the random variable is a binomial variable.