Question

You are analyzing the revenues of 3 IT companies (MBI, Letni and PH) over a period of 25 years. You find that the annual revenues of these companies have Normal Distributions. Interestingly, the average annual revenue is equal $6B for each of the three companies. However, the standard deviation of the annual revenue of MBI, Letni and PH is 1.2, 0.8 and 0.9, respectively. Match the shape of the Normal Distribution Curve of revenue with associated companies!

1. Steepest:

a. PH

b. Letni

C. MBI

D. It cannot be determined from the given information

2. Flattest

a. PH

b. Letni

C. MBI

D. It cannot be determined from the given information

Answer 1

Concept

• Mean is a measure of central tendency.
• Standard deviation tells the deviation of the data from the mean. Larger standard deviation with respect to mean gives a flatter graph and smaller standard deviation relative to mean gives a steeper graph

In this problem

MBI: Mean = 6, SD = 1.2

PH: Mean = 6, SD = 0.9

Letni: Mean = 6, SD = 0.8

1. So, the standard deviation is least in Letni, so Steepest curve is Letni, Option B

2. For the Flat curve, when the data is spread apart, meaning standard deviation is high, the curve is flat. So the curve of MBI is flattest, Option C

We can also plot the curves and verify. I have plotted the curves for these three values. PFB the curves

For MBI

For PH

For Letni

So from the curves also it is clear that MBI has the flattest and Letni has the steepest