Answer to Question #224218 in Statistics and Probability for Qasim

Question

In Gallup’s Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1214 people aged 18 and over. One of the questions was, “How many cups of coffee, if any, do you drink on an average day?” The following table shows the results obtained

Number of Cups per Day Number of Responses

0 465

1 364

2 193

3 91

4 or more 101

Define a random variable X = number of cups of coffee consumed on an average day.

Answer 1

Total problem

In Gallup’s Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1214 people aged 18 and over. One of the questions was, “How many cups of coffee, if any, do you drink on an average day?” The following table shows the results obtained Number of Cups per Day Number of Responses 0 465 1 364 2 193 3 91 4 or more 101 Define a random variable X = number of cups of coffee consumed on an average day. a) Develop a probability distribution for X. b) Compute the expected value of X. c) Compute the variance of X. 

a)

$P(x) = \frac{Number \;of \;persons}{Total\; number \;of \;persons}$

Probability distribution

b) Expected value of $X = \sum x \times P(x) = 0 + 0.299 + 0.317 + 0.224 + 0.332 = 1.175$

c) Variance of X $= \sum x^2 \times P(x) - \mu^2$

$= 2.939 - (1.175)^2 = 1.558$