Question 1195500: A manufacturer knows that their items have a normally distributed length, with a mean of 5.1 inches, and standard deviation of 0.5 inches.
If one item is chosen at random, what is the probability that it is less than 4.5 inches long?
Round your answer to three decimal places.
Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website! .
A manufacturer knows that their items have a normally distributed length,
with a mean of 5.1 inches, and standard deviation of 0.5 inches.
If one item is chosen at random, what is the probability that it is less than 4.5 inches long?
Round your answer to three decimal places.
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The normal distribution curve is a bell shaped curve.
The question is to determine the area under the GIVEN normal distribution curve to the left of the value 0.45 inches.
Go to website
https://onlinestatbook.com/2/calculators/normal_dist.html
and use free of charge online calculator specially intended for this purpose.
Input 5.1 in the port window " Mean ";
input 0.5 in the port window " SD "; ( <<<---=== SD means "standard deviation" )
input number 0.45 in the port window " BELOW ".
Then click the button " Recalculate ".
You will get the  0.1151 in the window " Area (probability) ".
The shaded area in the plot shows you the area of the interest.
Round the answer as necessary.
Every time as you get similar problem, you can solve it this way.
This way is the easiest and shortest way to learn the subject.
When you learn the subject enough, you will be ready and may start learning other ways.
. . . . . . . . . . . .
On HOW TO do it using pocket calculator, see this video lesson
https://www.youtube.com/watch?v=IyEKEL9nm28
and/or many other video lessons, which you can find in the Internet.
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