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A pizzeria offers three sizes of cola, small, medium, and large to accompany its pizza. Soft drinks cost $0.80, $0.90 and $1.20, respectively. Thirty percent of the orders correspond to the small size; 50%, to the medium, and 20%, to the large. Arrange the size of the soft drinks and the probability of sale into a probability distribution. a) Is it a discrete probability distribution? Please indicate why. b) Calculate the average amount charged per cola soft drink. c) What is the variance of the amount charged for a cola drink? What is the standard deviation?

A pizzeria offers three sizes of cola, small, medium, and large to accompany its pizza. Soft drinks cost $0.80, $0.90 and $1.20, respectively. Thirty percent of the orders correspond to the small size; 50%, to the medium, and 20%, to the large. Arrange the size of the soft drinks and the probability of sale into a probability distribution. a) Is it a discrete probability distribution? Please indicate why. b) Calculate the average amount charged per cola soft drink. c) What is the variance of the amount charged for a cola drink? What is the standard deviation?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A pizzeria offers three sizes of cola, small, medium, and large to accompany its pizza. Soft drinks cost $0.80, $0.90 and $1.20, respectively. Thirty percent of the orders correspond to the small size; 50%, to the medium, and 20%, to the large. Arrange the size of the soft drinks and the probability of sale into a probability distribution.
a) Is it a discrete probability distribution? Please indicate why.
b) Calculate the average amount charged per cola soft drink.
c) What is the variance of the amount charged for a cola drink? What is the standard deviation?

Expert Solution
Step 1: Introduce the given information

Here, the given information is :-

A pizzeria offers three sizes of cola, small, medium, and large to accompany its pizza. Soft drinks cost $0.80, $0.90 and $1.20, respectively. Thirty percent of the orders correspond to the small size; 50%, to the medium, and 20%, to the large

we know that ,

A Discrete probability distribution is a distribution where the random variable can only take on a finite or countable number of values and the sum of all Probabilities must be 1 

Using formula,

M e a n space equals mu equals space sum for blank of x times p left parenthesis x right parenthesis

v a r i a n c e space equals space sigma squared equals stack sum x squared with blank below p left parenthesis x right parenthesis space minus space sum for blank of open parentheses x times p left parenthesis x right parenthesis close parentheses squared

Standard deviation equals sigma equals square root of v a r i a n c e end root


    

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