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Intermediate Mathematics - Calculation of probabilities for a normal
distribution

Calculation of probabilities for a normal distribution

The "Normal distribution - cdf" table can be used in reverse to find the
value of the random variable for a given probability or area under the
curve. The name given to this value of the random variable is a Quantile.

The value of q will correspond to an area equal to 0.774 under the Normal
distribution graph.

The probability value 0.774 must be found in the 'body' of the "Normal
distribution - cdf" table. First, you look for a value close to, but
slightly smaller than, the required value. The appropriate section of the
general Normal distribution - cdf table is shown below.

_x_
3
4
5
6
1
2
3
4

0.6
0.7357
0.7389
0.7422
0.7454
3
6
10
13

0.7
0.7673
0.7703
0.7734
0.7764
3
6
9
12

0.8
0.7967
0.7995
0.8023
0.8051
3
6
8
11

Notice that the probability value 0.7734 in the body of the Normal
distribution - cdf table is slightly smaller than the required value 0.774.
The probability value 0.7734 is at the intersection of the row for x = 0.7
(first decimal place) and the column for x = 0.05 (second decimal place).
That is, the general x value equals 0.75 for the probability value 0.7734.

Notice that the probability value 0.006 in the body of the Normal
distribution - cdf table is in the column for x = 0.002 (third decimal
place).

When we add these two readings together for our case we find that the
general x value equals 0.752 for the probability value 0.7740 (0.7734 +
0.0006).

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