## Standard Normal Probability Distribution

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# Standard Normal Probability Distribution

Hi All,

I need some help to find out Standard Normal Probability Distribution .I tried various links and post in Google to find out out the answer but could not got what exactly what i am looking for .

So here is is what i am looking for .

If my computed Z value us 2.84 the area under the curve is .4977  and if it is 1 then its is .3413 as per the normal curve table.

I am unable to find out how to get this .4977 and .3413 when i have z value is 2.84 and 1 respectively .

I tried CPF and PDF function none of this giving me  .4977 and .3413.

Can any one of you help me to find out this answers .

Regards

KD

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Solution
‎11-14-2015 09:58 AM
Posts: 1,256

## Re: Standard Normal Probability Distribution

There are two slightly different types of "normal curve tables", more precisely: of tables of the cumulative distribution function (CDF) of the standard normal distribution N(0, 1): Some tabulate the actual cumulative distribution function F, which satisfies F(u)=P(X<=u) for a random variable X having a standard normal distribution (so that P(X<=u) is the probability that such a random variable takes a value less than or equal to u). Others tabulate, for non-negative u, the values of F(u) - 0.5, i.e. the probabilities P(0<X<=u). Your table is of the latter type.

Remember that the area under the bell-shaped curve representing the probability density function (PDF) of the standard normal distribution equals 1 and that it is symmetric about the y-axis, so that F(0)=P(X<=0)=0.5.

The SAS function CDF calculates values of cumulative distribution functions. In particular, CDF('NORMAL', u) returns F(u). As mentioned above, you have to subtract 0.5 in order to arrive at the values found in your table.

``````data _null_;
p=cdf('NORMAL', 2.84)-0.5;
put p 6.4;
run; /* 0.4977 */

data _null_;
p=cdf('NORMAL', 1)-0.5;
put p 6.4;
run; /* 0.3413 */
``````

PDF('NORMAL', u) returns the value of the standard normal probability density function. Its symmetry mentioned above means that PDF('NORMAL', u)=PDF('NORMAL', -u) for all numbers u. For calculating probabilities, CDF is the function to use.

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Solution
‎11-14-2015 09:58 AM
Posts: 1,256

## Re: Standard Normal Probability Distribution

There are two slightly different types of "normal curve tables", more precisely: of tables of the cumulative distribution function (CDF) of the standard normal distribution N(0, 1): Some tabulate the actual cumulative distribution function F, which satisfies F(u)=P(X<=u) for a random variable X having a standard normal distribution (so that P(X<=u) is the probability that such a random variable takes a value less than or equal to u). Others tabulate, for non-negative u, the values of F(u) - 0.5, i.e. the probabilities P(0<X<=u). Your table is of the latter type.

Remember that the area under the bell-shaped curve representing the probability density function (PDF) of the standard normal distribution equals 1 and that it is symmetric about the y-axis, so that F(0)=P(X<=0)=0.5.

The SAS function CDF calculates values of cumulative distribution functions. In particular, CDF('NORMAL', u) returns F(u). As mentioned above, you have to subtract 0.5 in order to arrive at the values found in your table.

``````data _null_;
p=cdf('NORMAL', 2.84)-0.5;
put p 6.4;
run; /* 0.4977 */

data _null_;
p=cdf('NORMAL', 1)-0.5;
put p 6.4;
run; /* 0.3413 */
``````

PDF('NORMAL', u) returns the value of the standard normal probability density function. Its symmetry mentioned above means that PDF('NORMAL', u)=PDF('NORMAL', -u) for all numbers u. For calculating probabilities, CDF is the function to use.

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Posts: 108