#451 A day’s sales in $1000 units at a gas station

A day’s sales in $1000 units at a gas station - Math

ChemistryExplain daily providing Q&A content “#451 A day’s sales in $1000 units at a gas station" in Bridges math curriculum, Dr mather, Carnegie math, 10th maths, 10th grade math problems, Math

Get the Free Online Chemistry Q&A Questions And Answers with explain. To crack any examinations and Interview tests these Chemistry Questions And Answers are very useful. Here we have uploaded the Free Online Chemistry Questions. Here we are also given the all chemistry topic.

 ChemistryExplain team has covered all Topics related to inorganic, organic, physical chemistry, and others So, Prepare these Chemistry Questions and Answers with Explanation Pdf.

For More Chegg Questions

• Inorganic Chemistry
• Organic Chemistry
• Physical Chemistry

Free Chegg Question

A day’s sales in $1000 units at a gas station have a gamma distribution with parameters k = 5 and λ = 0.9.

(a) What is the expectation of a day’s sales?

---

(b) What is the standard deviation of a day’s sales?

---

(c) What are the upper and lower quartiles of a day’s sales?

---

(d) What is the probability that a day’s sales are more than $6000?

(This problem is continued in Problem.)

Problem

Recall Problem in which a day’s sales in $1000 units at a gas station have a gamma distribution with k = 5 and λ = 0.9. If the sales on different days are distributed independently of each other, estimate the probability that in one year the gas station takes in more than $2 million.

Free Chegg AnswerFor More Chemistry Notes and Helpful Content Subscribe Our YouTube Chanel - Chemistry Explain  

Free Chegg Answer

1. Step 1 of 5

   A day’s sales in $1000 units (X) at a gas station have a gamma distribution with parameters  and .

   The probability distribution of X is given as follows:

   

2. Step 2 of 5

   (a)

   The expectation of gamma distribution is given by .

   Therefore, the expectation of a day’s sales is calculated as follows:

   

3. Step 3 of 5

   (b)

   The standard deviation of gamma distribution is given by .

   Therefore, the standard deviation of a day’s sales is calculated as follows:

   

4. Step 4 of 5

   (c)

   The upper quartile is given as follows:

   

   The requirement is thus to obtain  such that 75% of the data points are below X.

   The upper quantile in EXCEL is obtained by formula , which gives the result 6.97159.

   Hence, the upper quantile is .

   The lower quartile is given as follows:

   

   The requirement is thus to obtain  such that 25% of the data points are below X.

   The lower quantile in EXCEL is obtained by formula , which gives the result 3.742889.

   Hence, the lower quantile is .

5. Step 5 of 5

   (d)

   The probability that a day’s sales are more than $6000 is calculated as follows: