Question

Open the Excel program

Suppose we want to know the standard normal distribution up to the given value.

That is P(Z < a). Lets use Excel instead of the standard normal distribution table

In cell A1 type mean. In cell B1 type 0. That means that we are letting mean be zero.

click on cell A2 and type SD. In cell B2 type 1. That means that we are letting standard deviation be one. That is, the normal distribution is standard.

Suppose that a=-1.72.

Click on cell B6 and type =NORMDIST(-1.72,B1,B2,TRUE).

We obtained in B6 the probability of Z<-1.72. Compare this result with what you would find in the standard normal distribution table.  

Now we do it for any normal distribution. That is, not only that we do not need the table, but we also do not have to do the algebra to go from standard normal distribution to the given normal distribution. We will illustrate that on an example. Suppose that SAT scores have normal distribution with mean 840 and standard deviation 200. If you score 970 on the SAT, what is your percentile? To do this we first go to cell D1and type 840. That means that we are letting mean be 840.

Click on cell D2 and type 200. That means that we are letting standard deviation be 200. That is, the normal distribution is not standard.

Now click on cell D6 and type =NORMDIST(970,D1,D2,TRUE). Did you obtain approximately 74 as your percentile?

Exercises

Exercise 1 Using Excel, evaluate P(Z<1.34236). Put your result in cell A10.

Exercise 2 Find the table value T(1.34236) by looking at the table. Put the value you found in the table in cell A12.

Exercise 3 Compare your result in cell A12 with your result in cell A10. Put your explanation in cell A13.

Exercise 4. If X is normally distributed with mean 890 and standard deviation 150 evaluate P(X<1048) using Excel. Put your result in cell A14.

Answer 1

Now we do it for any normal distribution. That is, not only that we do not need the table, but we also do not have to do the algebra to go from standard normal distribution to the given normal distribution. We will illustrate that on an example. Suppose that SAT scores have normal distribution with mean 840 and standard deviation 200. If you score 970 on the SAT, what is your percentile? To do this we first go to cell D1and type 840. That means that we are letting mean be 840.

By using this command in excel,

=NORMDIST(970,D1,D2,TRUE)

I get the value 0.74.

Exercise 1 Using Excel, evaluate P(Z<1.34236).

P(Z < 1.34236) = 0.9103

Exercise 2 Find the table value T(1.34236) by looking at the table.

The table value for 1.34236 is 0.9099.

Exercise 3 Compare your result in cell A12 with your result in cell A10. Put your explanation in cell A13.

The result is excel is larger than result in table.

Exercise 4. If X is normally distributed with mean 890 and standard deviation 150 evaluate P(X<1048) using Excel. Put your result in cell A14.

z-score for x = 1048 is,

z = (x - mean) / sd = (1048 - 890) / 150 = 1.05

Now we have to find P(Z < 1.05)

Now we will use same syntax as,

=NORMSDIST(z)

where z = 1.05

P(Z < 1.05) = 0.8531