The cost per item at a supermarket follows an exponential distribution. There ar

Question

The cost per item at a supermarket follows an exponential distribution. There are many inexpensive items and a few relatively expensive ones. The mean cost per item is $9.00. What is the percentage of items that cost: A. Less than $6.00? (Round your answer to 4 decimal places.) B. More than $10.00? (Round your answer to 4 decimal places.) C. Between $7.00 and $9.00? (Round your answer to 4 decimal places.) D. Find the 45th percentile. Fifty five percent of the supermarket items cost more than what amount? (Round your answer to 2 decimal places.)

Explanation / Answer

This is exponential distribution with mean=9

a.

The following information is provided:

The provided mean is =9.

We need to compute Pr(X6). Therefore, the following is obtained:

Pr(X>=6) = e^{-6/9} = 0.5134

so P(x<6)=1-0.5134=0.4866

b,

The following information is provided:

The provided mean is =9.

We need to compute Pr(X10). Therefore, the following is obtained:

Pr(X10)=1e10/9=0.6708

so P(x>10)=1-0.6708=0.3292

c. P(7<x<9)=

The following information is provided:

The provided mean is eta= 9=9.

We need to compute Pr(7X9). Therefore, the following is obtained:

Pr(7X9)=Pr(X9)Pr(X7)= e^{-7/9} - e^{-9/9} = 0.4594 - 0.3679 =0.0915

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