Question

Use the data below (ie. copy and paste into Excel) to build a CDF. Using the CDF you've built, what is the probability that your sales are $12M or less? (each data point is separated by a single space)

Sales ($ks)

10541 8991 5905 8251 11461 6924 7347 10972 7811 10559 9825 9130 5116 7830 8388 8588 6945 7697 9655 11516 11952 13547 9168 11942 9917 10666 9717 13457 10319 9731 10279 7202 12103 11482 11944 9188

Answer 1

Solution:

The frequency distribution, probability distribution, and Cumulative distribution function (CDF) for the given data by using excel is given as below:

Sale ($M)	Frequency	Probability	CDF
≤ 6	2	0.0556	0.0556
6 to 7	2	0.0556	0.1111
7 to 8	5	0.1389	0.2500
8 to 9	4	0.1111	0.3611
9 to 10	8	0.2222	0.5833
10 to 11	6	0.1667	0.7500
11 to 12	6	0.1667	0.9167
12 to 13	1	0.0278	0.9444
13 to 14	2	0.0556	1.0000
Total	36	1.0000

The histogram for the above frequency distribution is given as below:

From this histogram, it is observed that the variable sale follows an approximately normal distribution.

Now, we have to find the P(X≤12)

So, by using the above table, we have

P(X≤12) = 0.9167

Required probability = 0.9167