Question

1. Explain the inputs (and outputs if you know them) of the following Excel functions:

   • Norm.S.Dist(). • Norm.Inv().
   • T.Dist().

Answer 1

NORM.S.DIST(z,cumulative)

The NORM.S.DIST function syntax has the following arguments:

• Z     Required. The value for which you want the distribution.

• Cumulative     Required. Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, NORMS.DIST returns the cumulative distribution function; if FALSE, it returns the probability mass function.

Example

=NORM.S.DIST(1.333333,TRUE)  

output

0.908788726

so basically it finds p(x<=1.333) when x follows standard normal distribution with mean 0 and variance = 1

2)

Norm.Inv()

Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.

Syntax

Norm.Inv(probability,mean,standard_dev)

The NORMINV function syntax has the following arguments:

• Probability     Required. A probability corresponding to the normal distribution.

• Mean     Required. The arithmetic mean of the distribution.

• Standard_dev     Required. The standard deviation of the distribution.

Remarks

• If any argument is nonnumeric, NORMINV returns the #VALUE! error value.

• If probability <= 0 or if probability >= 1, NORMINV returns the #NUM! error value.

• If standard_dev ≤ 0, NORMINV returns the #NUM! error value.

• If mean = 0 and standard_dev = 1, NORMINV uses the standard normal distribution

Data

Description

0.908789

Probability corresponding to the normal distribution

40

Arithmetic mean of the distribution

1.5

Standard deviation of the distribution

Formula

Description

Result

=NORMINV(A2,A3,A4)

Inverse of the normal cumulative distribution for the terms above

42.000002

3)

T.Dist()

Returns the Student's left-tailed t-distribution. The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.

Syntax

T.DIST(x,deg_freedom, cumulative)

The T.DIST function syntax has the following arguments:

• X     Required. The numeric value at which to evaluate the distribution

• Deg_freedom     Required. An integer indicating the number of degrees of freedom.

• Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, T.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Remarks

• If any argument is nonnumeric, T.DIST returns the #VALUE! error value.

• If deg_freedom < 1, T.DIST returns an error value. Deg_freedom needs to be at least 1.

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Formula	Description	Result
=T.DIST(60,1,TRUE)	Student's left-tailed t-distribution for 60, returned as the cumulative distribution function, using 1 degree of freedom.	0.99469533
=T.DIST(8,3,FALSE)	Student's left-tailed t-distribution for 8, returned as the probability density function, using 3 degrees of freedom.	0.00073691