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# A catalyst researcher states that the diameters, in ISBN: 9780073401331 38

## Solution for problem 3E Chapter 4.7

Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

A catalyst researcher states that the diameters, in microns, of the pores in a new product she has made have the exponential distribution with parameter λ=0.25

a. What is the mean pore diameter?

b. What is the standard deviation of the pore diameters?

c. What proportion of the pores are less than 3 microns in diameter?

d. What proportion of the pores are greater than 11 microns in diameter?

e. What is the median pore diameter?

f. What is the third quartile of the pore diameters?

g. What is the 99th percentile of the pore diameters?

Step-by-Step Solution:

Step 1 of 7</p>

The new product have the exponential distribution with The pmf of exponential distribution is The CDF of exponential distribution is a) Here we have to find the mean pore diameter

The mean of exponential distribution is =1/0.25

=4

Hence mean of pore diameter is 4 microns

Step 2 of 7</p>

b) Here we have to find standard deviation of pore diameter

The standard deviation of pore diameter is = =4

Hence the standard deviation of pore diameter is 4 microns

Step 3 of 7</p>

c) Here we have to find probability of less than 3 microns

Then P(X<3)=1- =1-0.4724

=0.5276

Hence the probability of less than 3 microns is 0.5276

Step 4 of 7</p>

d) Here we have to find probability of more than 11 microns

Then P(X>11)=1-P(X 11)

=1-(1- )

= =0.064

Hence the probability of more than 11 microns is 0.064

Step 5 of 7

Step 6 of 7

##### ISBN: 9780073401331

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