Question

According to Southern California Edison(SCE) the mean electricity consumption during winter is 1650 kwh per month in Los Angeles area. Assume electric consumption have a normal distribution with a mean of 1650 kwh and a standard deviation of 320 kWh. SCE sent a notice to you informing that about 90% of the households use less electricity than you do.

a. what is your monthly electricity consumption?

b. Assume SCE conducted a telephone survey In Los Angeles area between December 2019 in January 2020 . according to the survey, 74% of consumers said SCE provided a satisfactory service. Assume that this result holds true for the current population of Los Angeles area. Let X denote the number of consumers in a random sample of three who hold the said opinion. Write the probability distribution of X, in draw a bar graph for x values of 0, 1, 2, and 3.

Answer 1

(b) Now, p = probability of a consumer saying that SCE provided a satisfactory service = 74% = 0.74.
n = sample size of consumers = 3.
Now, X = no. of cosumers in a random sample of 3 who say that SCE provided a satisfactory service.
X ~ Binomial(n = 3, p = 0.74).
The probability distribution (pmf) of X = P(X = x) = .
The values of the probability distribution of X at x = 0,1,2,3 are = (0.0176, 0.1501, 0.4271, 0.4052).
The bar graph is given below.