1. The customer satisfaction survey of a major automobile manufacturer has the f

Question

1. The customer satisfaction survey of a major automobile manufacturer has the following 1-5 scale:

1 – SD [strongly Disagree] 2 – D [Disagree] 3 – N [Neutral] 4 – A [Agree} 5 – SA [ Strongly Agree]

Every customer of the vehicle is asked to rate the following statement: “I am satisfied with the overall reliability of this vehicle.” The results of the survey yield the following distribution of answers, where the variable X is the satisfaction level chosen by a randomly selected customer

X=x 1 2 3 4 5

P(X=x ) 0.15 0.25 0.35 0.20 p

(a) Find the correct value of the probability P(X = 5) = p in the above distribution table.

(b) Suppose a customer is randomly selected from the population. What is the probability that his or her level of satisfaction with the automobile is 3?

(c) Suppose a customer is randomly selected from the population. What is the probability that his evaluation is larger than 3?

(d) What is the population mean, µX, for the random variable X ?

(e) Find the population variance, X 2 , and standard deviation of X.

Explanation / Answer

The sum of probabilities will be equal to 1, thus 0.15+0.25+-.35+0.2+p=1 or 0.95+p=1 or p=0.05, P(x=3)=0.35, the probability P(x>3)=P(x=4)+P(x=5)=0.2+-.05=0.25, The mean is E(x)=sum(x*P(x)) and Variance=Sum(x^2*P(x))-E(x)^2,

thus mean=1*0.15+2*0.25+3*0.35+4*0.2+5*0.05=2.75

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