Solution Found!
A catalyst researcher states that the diameters, in
Chapter 4, Problem 3E(choose chapter or problem)
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 \(\lambda) = 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?
Equation transcription:
Text transcription:
\lambda
Questions & Answers
QUESTION:
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 \(\lambda) = 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?
Equation transcription:
Text transcription:
\lambda
ANSWER:Solution
Step 1 of 7
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