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# CALC 1 Normal Distribution Calculator

This calculator performs calculations involving the Normal Distribution including the CDF and inverse, Z-Tests, Z-Interval, PDF plotting, normal probability plots, histograms plots, box plots, normally distributed random numbers, percentile and inverse percentile.
Values for the tests and confidence intervals can use data calculated from lists or entered data. ## Calculator Keys Summary

Tap the link on the key name for an example.

Φ(z) - Calculates or stores the CDF for the values stored in z, x̄, s and n.

z- Calculates or stores the inverse CDF for the values stored in Φ(z), x̄, s and n.

- Calculates (from the values in listx) or stores the mean.

s - Calculates (from the values in listx) or stores the standard deviation.

n - Calculates (from the values in listx) or stores the number of samples.

nrmPrb - Plots a normal probability plot of the data in list x.

hist(b) - Plots a histogram of the data in list x with the number of bins in rgx.

zT(μ0) - Calculates the z Test using the values in x̄, s and n with μ0 in rgx.

z int(cl) - Calculates the confidence interval for the confidence level in rgx using the values in x̄, s and n.

Σ+ - Appends the current number in rgx to list x. See the Data Entry Overview for other ways to enter data.

### Shifted Keys

P<zT(μ0) - Plots the z Test for <μ0 using the values in x̄, s and n with μ0 in rgx.

P>zT(μ0) - Plots the z Test for >μ0 using the values in x̄, s and n with μ0 in rgx.

P≠zT(μ0) - Plots the z Test for ≠μ0 using the values in x̄, s and n with μ0 in rgx.

r norm - Fills list x with normally distributed random numbers based on values stored in x̄, s and n.

box - Displays a box plot of the data in list x.

box(n) - Displays n box plots of the data in lists a - e based on the value in rgx.

P(<z) - Displays a plot of the PDF based on the values in z, x̄, s and n shading the area < z. (Lower tail)

P(>z) - Displays a plot of the PDF based on the values in z, x̄, s and n shading the area > z. (Upper tail)

P(<z>) - Displays a plot of the PDF based on the values in z, x̄, s and n shading the area <z and >z. (two tails)

P(>z<) - Displays a plot of the PDF based on the values in z, x̄, s and n shading the area > -z and < z.

sum stats - Calculates summary stats for the data in list z. The values can be views in the History Detail by tapping the (i) button on the toolbar.

sort 0-9/9-0 - Sorts list x ascending or descending.

prcntl(x) - Calculates the percentile (percentileInc()) of rgx for list x. Entering 0.5 will calculate the median, 0.25 will calculate the first quartile.

prcntl⁻¹(x) - Calculates the inverse percentile of rgx for list x.

std(x) - Calculates the standard score of x based on the values x̄, s .