As a special promotion, a fast food chain gives a prize ticket to each customer.
ID: 3154085 • Letter: A
Question
As a special promotion, a fast food chain gives a prize ticket to each customer. Customers scratch the tickets to reveal a hidden prize. Twenty percent of the tickets are worth $2 off their next purchase; twenty percent are worth $1 off; and the rest say "Thanks for playing. Please come again. Make a table for the probability distribution for x = the value of one randomly selected ticket. Find the mean of the distribution of x. What is the practical significance of the mean for the fast food chain Find the variance and standard deviation for x. The nine possible samples of size 2 are listed in the table above. Complete the tabic with the probability and the mean for each sample. Make a table for the probability distribution of x bar. Find the mean of the distribution of x bar. How does it compare to the mean for x Find the variance of the distribution of x bar. How does it compare to the variance of xExplanation / Answer
a. The table for the probability distribution for x is
b) Mean of x = 0*0.6 + 1* 0.2 + 2* 0.2 = 0.6
if you visit the fast food chain large number of times you will get an average prize of worth $0.6
c) variance of x is sum of x^2 * P(x) - (mean)^2
=0*0.6 + 1* 0.2 + 4* 0.2 -(0.6)^2 = $0.64
standard deviation = sqrt(variance) = sqrt($0.64) = $0.8
d)
e) Probability distribution of x bar using the above sampling distribution of x is
f)
mean of the distribution of x bar = 0*0.36 + 0.5*0.24 + 1* 0.28 + 1.5*0.08 + 2* 0.04 = $0.6
the mean of x bar = mean of x
g) variance of distribution of x bar = sum of xbar^2 * P(x) - (mean of x bar) ^2
= 0*0.36 + 0.25*0.24 + 1* 0.28 + 2.25*0.08 + 4* 0.04-(0.6)^2 = $0.32
variance of x = $0.64
variance of x bar = $0.64/2 = $0.32 = variance of x / sample size
Variance of x bar is variance of x divided by sample size
X P(x) $ 0.00 0.6 $ 1.00 0.2 $ 2.00 0.2Related Questions
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