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Chapter 6: 2.2 (page 349)

Compute and interpret the standard deviation ofX.

Short Answer

Expert verified

The standard deviation is5.423.

Step by step solution

01

Given information

A large auto dealership keeps track of sales made during each hour of the day. LetX= the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of is as follows:

We need to compute the standard deviation ofX.

02

Explanation

Given:

From example, the probability distribution is:

X
0
1
2
3
4
5
6
7
8
10
P(X)0.001
0.006
0.007
0.008
0.012
0.2
0.038
0.099
0.319
0.053

We can compute the standard deviation by using following formula

localid="1649919082471" σ=∑x2×P(x)−∑x2×P(x)2=02(0.001)+12(0.006)+….+102(0.053)−(8.28)=5.423

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