Find the percentage of values that lie between

and

:

Between

and

:

Between

and

:

Package it up as a function:

Compute

-values for a

-test with alternative hypothesis

:

Alternative hypothesis

:

Alternative hypothesis

:

A battery has a lifetime that is approximately normally distributed with a mean of 1000 hours and a standard deviation of 50 hours. Find the fraction with a lifetime between 800 and 1000 hours:

Out of 100 batteries, compute how many have a lifetime between 800 and 1000 hours:

Coffee beans are sold in 5 lb sacks that have true weight normally distributed with a mean of 5 lbs and a variance of 0.01 lb

. Find the probability that a given sack weighs at least 4 lbs, 15 oz:

This can be directly computed from the

SurvivalFunction:

A company manufactures nails with length normally distributed, mean 0.497 inches, and standard deviation 0.002 inches. Find the fraction that satisfies the specification of length equal to 0.5 inches plus/minus 0.004 inches:

Direct computation with

CDF:

A company manufactures nails with length normally distributed and a mean of 0.5 inches. If 50% of the produced nails have lengths between 0.495 and 0.505, find the standard deviation:

Find the standard deviation:

A sample is selected from a distribution with mean 5 and standard deviation 1.5. Find the minimum size

of the sample so that with probability 0.97 the sample mean is within 0.8 of the distribution mean:

The probability as a function of sample size:

Find the minimum sample size

:

The weight of a person including luggage has normal distribution with mean 200 and standard deviation 40. A plane's load limit is 10000 lbs and it can take 42 passengers. With the maximum number of passengers on board, what is the probability of the plane being overloaded?

Normally distributed points in the plane:

Normally distributed points in 3D: