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# Probability distribution assignment question

We are now going to use Excel to make a probability table and find the mean and sd. We would like to know how many pets people have in an apartment building called Pets Paradise. A survey completed by all apartment residents show that there are 84 apartments with no pets, 35 apartments with 1 pet and 11 apartments with 2 pets.

We put our data in rows 1 and 2. In Cell A1 we type pets and in cell A2 we type apartments. Now we type our data, 0 in B1, 1 in C1, 2 in D1, 84 in B2, 35 in C2 and 11 in D2.

Second row is frequencies and you will now make it probabilities. First let’s get our population size. Enter population size in F1 and enter =b2+c2+d2 in F2. Probability table will be located in rectangle A4-D5. First enter X(pets) in A4 and p(X) in A5. Now enter 0 in B4, 1 in C4, 2 in D4. Then enter =B2/F2 in B5.

Exercise 1. Complete this probability table.

Exercise 2. Verify that area A4-D5 represents a probability distribution. Are all probabilities in B5, C5 and D5 nonnegative? Enter yes or no in cell G5. Is the sum of all probabilities equal to 1? Enter sum in F4 and evaluate the sum of all probabilities in cell F5. Enter probability distribution or not a probability distribution in H5.

Now we start working on mean and sd. We will move our data into vertical format. Enter p(x) in A7 and X in B7. Enter =b4 in b8, =c4 in B9 and =d4 in b10. Similarly, enter =b5 in a8, =c5 in a9 and =d5 in a10.

Enter MEAN in a12 and in C7, and calculate mean in B12 by entering formula =A8*B8+A9*B9+A10*B10

Enter ID in d7 and SID in e7.

Exercise 3. Complete the table in the rectangle a7-e10 .

Enter VARIANCE in a13 and SD in A14.

Exercise 4. Evaluate variance and SD and put the corresponding formulas in B13 and B14.