Download Lab 8

MATH 105 Lab -- Normal distributions
The goal of this lab is to compute normal probabilities and inverse normal probabilities
using Excel.
The Excel functions we consider are:
=NormSDist(a) which computes the probability that z  a in the Normal Standard
distribution
=NormDist(a,m,s,0) which computes Pr(a) in the normal distribution with mean m and
standard deviation s,
=NormDist(a,m,s,1) which computes the cumulative Pr(xa) in the normal distribution
with mean m and standard deviation s, (Note: the cumulative probability is obtained
when the 4th argument is set to 1 instead of 0.)
=NormInv(p,m,s) gives the value of x so that NormDist(x,m,s,1) equals p in the normal
distribution with mean m and standard deviation s,
Problem 1. In this problem you will compute Pr(azb) for values of a and b using the
Standard Normal distribution. The probability that z lies between a and b is found by
substracting the cumulative probabilities, that is
=NormSDist(b)
- NormSDist(a)
A. Compute Pr(-1z1) by entering =NormSDist(1) - NormSDist(-1) in a cell. Label
the probability.
B. Now compute Pr(-2z2) in another cell. Label this probability as well. In a text box
explain a "rule-of-thumb" suggested by these two calculations.
Although we used the NormSDist function above the same process can be used to
compute Pr(azb) for general normal distributions using NormDist(x,m,s,1).
Problem 2. Suppose X is normal distribution with mean 100 and standard deviation 15.
A. Compute Pr(x120) using appropriate values in NormDist(x,m,s,1).
B. Use the transformation z=(x-m)/s to convert 120 for the normal distribution to an
appropriate z-value for the Standard Normal distribution. Label the x and z values.
C. Compute Pr(zb) where b is the z-value found in Part B. (Remember to use the
NormSDist function for this.) Label the probability. Compare the results in Parts A and C
and in a text box explain the significance.
Problem 3. In this problem you are to see how the NormInv function works. Let X be a
normal distribution with mean 100 and standard deviation 20.
A. We want to find the x so that 40% of the distribution values are below it, that is, we
want to find the value that gives the 40th percentile. To find this x, enter the formula
=NormInv(0.4,100,20) in a cell and label it. Next, check that it works by computing
NormDist(x,100,20,1) where x is the value just found. What does it give? Lable it.
B. Find the x so that 20% of the distribution values exceed it. Label the value and check
it.