Solution Found!
The intake valve clearances on new engines of a certain
Chapter 4, Problem 9SE(choose chapter or problem)
The intake valve clearances on new engines of a certain type are normally distributed with mean 200 \(\mu m\) and standard deviation 10 \(\mu m\).
a. What is the probability that the clearance is greater than 215 \(\mu m\)?
b. What is the probability that the clearance is between 180 and 205 \(\mu m\)?
c. An engine has six intake valves. What is the probability that exactly two of them have clearances greater than 215 \(\mu m\)?
Questions & Answers
QUESTION:
The intake valve clearances on new engines of a certain type are normally distributed with mean 200 \(\mu m\) and standard deviation 10 \(\mu m\).
a. What is the probability that the clearance is greater than 215 \(\mu m\)?
b. What is the probability that the clearance is between 180 and 205 \(\mu m\)?
c. An engine has six intake valves. What is the probability that exactly two of them have clearances greater than 215 \(\mu m\)?
ANSWER:Answer:
Step 1 of 3:
(a)
In this question we have asked to find the probability that the clearance is greater than 215 .
Given Data:
Mean = 200
Standard deviation = 10
Intake valve clearances (X ) are normally distributed.
Hence
Here we will use the standard normal distribution table for the probability value calculation.
We can write,
Hence the z score of 215 is = 1.5 and corresponding area from the table is 0.9332
Since we have asked ), which is equal to the right of standard normal curve area.
And the value given into the table is left area of the standard normal curve so the area to the right is 1 - 0.9332 = 0.0668 since total area is equal to 1.
Therefore the probability that the clearance is greater than 215 is equal to 0.0668.