Intermediate Mathematics - Calculation of probabilities for a normal
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
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.
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
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 +
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