How to Read Normal Distribution Tables in Reverse PDF

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Reading normal distribution...

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How to Read Normal Distribution Tables in Reverse. This method is for questions of the type:

‘Find a if P(Z < a ) = 0.0287’

Vocabulary: Left side side

Right

P(Z < a ) = 0.0287 This is the

Shade

Use this Method: Step A:

First find out whether a is positive (+) or negative (-) by drawing a graph: To find the position of a • Decide which area you need to shade: o If you want P(Z < a ) shade the left side o If you want P(Z > a ) shade the right side •

•

•

Step A: First draw a graph • We want P(Z < a ) so we will shade the left side. • 0.0287 < 0.5 so we will shade a small area. So our graph will look like this:

Decide whether the probability given is more than 0.5 or less than 0.5 o If the probability is more than 0.5 you will need to shade a large area o If the probability is less than 0.5 you will need to shade a small area From your graph you will be able to say if a is positive (+) or negative (-)

Step B: •

Example: Find a if P(Z < a ) = 0.0287

Now find the value of a

If the probability is more than 0.5 look it up in the table If the probability is less than 0.5: o Calculate : 1 – probability o Look your answer up in the table

Step C:

Use your answers to Step A and Step B to find your final answer:

SO a IS NEGATIVE Step B:

Find the value of a • 0.0287 < 0.5 so ° Calculate 1 – 0.0287 = 0.9713 ° Look this up in the table to give 1.9 Step C: Use Step A and Step B to give your final answer. a is negative with value 1.9 FINAL ANSWER:

Further Examples 1) Find b if P (Z > b) = 0.7357

Step A:

First draw a graph.

•

We want P (Z > b) so we will shade the right side.

•

0.7357 > 0.5 so we want a large area

So the graph will look like this:

a = - 1.9

Right side large

b SO b IS Step B: •

Calculate the value of b

0.7357 > 0.5 so we can look up the value of b in the table. This gives 0.63 Using Step A and Step B the final answer is b = - 0.63

Step C:

2) Find c if P (Z > c) = 0.3783

Step A:

First draw a graph.

•

We want P (Z > c) so we will shade the right side.

•

0.3783 < 0.5 so we want a small area

So the graph will look like this: Right side small

c SO c IS Step B: •

Calculate the value of c

0.3783 < 0.5 so

Step C:

o

we calculate 1 – 0.3783 = 0.6217

o

look up the value of c in the table. This gives 0.31 Using Step A and Step B the final answer is c = + 0.31...