# Assignment 1 (Probability)

*label*Mathematics

*timer*Asked: Jul 1st, 2018

*account_balance_wallet*$15

**Question description**

The instructions and questions is in the attachment below. If you have any questions, please ask. Thanks

## Tutor Answer

my solution is 100% done, and attached below

MATH 153

T. McKoy

Summer 2018 Project 3 – Probability – Distributions - Normal

Context: It is now time to look at the McKoy family’s BGE data through the lenses of probability and

distributions. The list of data is not required for this project. You will look at a two-way table

(contingency table) based on months and average daily usage, as well as a list of random variable

outcomes and the probability of their occurrences. Finally, the binomial and the normal distributions

are applied to answer questions about the probability of specific outcomes. As usual, provide complete

and clear responses to the questions below.

PROBABILITY

Low Usage

Medium Usage

High Usage

Total

Jan – Apr

5

20

27

52

May – Aug

33

19

0

52

Sep – Dec

20

26

6

52

Total

58

65

33

156

The above contingency table summarizes the average daily usages on all of the McKoy family’s BGE bills

from January 2005 to December 2017. The years were divided into 3 equal parts consisting of four

months and this is represented by the first column. Each row shows the number of months in the

grouping that was classified by a specific usage category (low, medium, or high). Of course, the entire

table shows the interaction between these two variables. Use this table to respond to the following

questions.

1. If one of the BGE bills was selected at random, based on the marginal distributions, what is the

probability of the bill being categorized as Low Usage?

Answer:

The total number of bills categorized as Low Usage is 5 + 33 + 20 = 58 bills, and there is a total of 156

bills. Hence, the probability of the bill being categorized as Low Usage is equal to

P ( Low Usage ) =

58

= 0.3718

156

2. Provide the conditional distribution for the usage category based on the monthly grouping.

Answer:

The conditional distribution for the usage category can be provided as follow:

MATH 153

T. McKoy

Summ...

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