A restaurant chain routinely surveys customers and, among other questions, asks

Question

A restaurant chain routinely surveys customers and, among other questions, asks each customer whether he or she would return and rate the quality of food. Summarizing hundreds of questionnaires produced the table of joint probabilities below. 1. Rating Customer will return Customer will not return Poor Fair Good Excellent 0.02 0.08 0.35 0.20 0.10 0.09 0.14 0.02 What is the modal outcome in this survey? quality rating of the restaurant's food? food as good or excellent a. b. Create a marginal probability distribution for the random variable 'rating of food c. What proportion of customers say that they will return and give an unfavourable d. What proportion of customers who say that they will return, rate the restaurant's

Explanation / Answer

(A)

Table shows that proprotion is highest for category "Customer will return and food is good". So modal outcome in survey is  "Customer will return and food is good".

(B)

Following table shows row total and column total:

Following table shows the marginal distribution of food quality:

(c)

The required proprotion is

P(they will return and rate food quality as poor) = 0.02

(d)

P(good or excellent) = P(good) + P(excellent) = 0.49 + 0.22 = 0.71

P(they will return and good or excellent) = P(they will return and good)+P(they will return and excellent) =0.35+0.20 = 0.55

So requried proporiton is

P(they will return | good or excellent) = P(they will return and good or excellent) / P(good or excellent) = 0.55 / 0.71 = 0.7746

Cutomer will return Customer will not return Total Poor 0.02 0.1 0.12 Fair 0.08 0.09 0.17 Good 0.35 0.14 0.49 Excellent 0.2 0.02 0.22 Total 0.65 0.35 1

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