Question

These are the hourly salaries od all workers employed at the Manhattan Law Firm together with the probabilities

hourly salary in dollars	8	90	125	180	350
probability (distribution) of having such a salary	.1	.2	.5	.1	.1

The standard deviation for this salary distribution is approximately

Answer 1

Answer

we have the following data

x	P(x)
8	0.1
90	0.2
125	0.5
180	0.1
350	0.1

First, we need to find the mean

we know mean =

r P(z)

setting the values, we get

Mean=

μ (8 * 0.1) + (90 * 0.2) + (125 * 0.5) + (180 * 0.1) + (350 * 0.1) = 134.3

Now, the formula for standard deviation is given as

setting the given values, we get

νΊδ2 * 0.1) + (902 * 0.2) + (125? * 0.5) + (1802 * 0.1) (3502 * 0.1)]-(134.3)2 σ

on solving, we get

σ = V/24928,9| _ 18036.49 = V689241-83.02

So, the required standard deviation for this salary distribution is approximately is 83.02 (rounded to 2 decimals)