Math Is Fun Forum

MathNewbie22

Member

Registered: 2013-04-22

Posts: 4

Probability

A set of final exam marks in a stats course is normally distributed, with a mean of 73 and a standard deviation of 9.
What is the probability that a student scored below 85 on this exam? Round to 4 decimal places as needed.

I don't understand this question either. Any help would be much appreciated ~~"..

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Probability

hi MathNewbie22,

Take a look at

http://www.mathsisfun.com/data/standard … table.html

This normal graph is brilliantly interactive.  You slide the z value about and it gives you the probability as a percentage.

For your question you need to choose the display option 'up to z'

Now to decide what z is for your question.

Clearly, you couldn't have a separate graph for every possible mean and every possible standard deviation.  You'd need an infinite number of them!!!

So statisticians have just one, the standard normal graph, which has a mean of zero and a sd. of 1.

So you have to convert your question into the standard graph version.

The score is 85 so it is 85 - 73 from the mean.

So imagine the whole graph shifted 73 places left.  Now the mean is at zero and your 85 has become 12

So the equivalent question would be a mean of zero and a score of 12.

But the sd. is also wrong.  The graph needs rescaling so that it has a sd. of 1.

You do that by dividing by 9.

Thus mean 73, sd 9 and score 85 becomes mean 0, sd. 1 and score

On the graph move the sllder until you get this z value and there's the probability.

In an exam they won't let you carry a computer in and go on-line, so how do you do the question then?

Look below the graph and you'll find a table of probabilities for given z values.

This table starts at the half way value of z = 0 and goes up to a z value of 3.09.  It saves space by not giving the other half of the table, which would be the same by symmetry.

So you look for your z value, read off the probability, and add 0.5 for the missing half of the table.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob