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Chapter 6: Q.16 (page 355)

Kids and toys Refer to Exercise 4. Calculate and interpret the standard deviation of the random variable X. Show your work.

Short Answer

Expert verified

The number of toys played with is on average 1.3106 toys from the mean.

Step by step solution

01

Given Information

Given in the question that, the probability distribution of the number Xof toys played with by a randomly selected subject is as follows:

02

Explanation

The expected value is computed by adding each possibility by its probability:

E(X)=∑xP(x)=0×0.03+1×0.16+2×0.30+3×0.23+4×0.17+5×0.11=2.68

The expected value of the squared variation from the mean is the variance:

σ2=∑(x-μ)2P(x)=(0-2.68)2×0.03+(1-2.68)2×0.16+(2-2.68)2×0.30+(3-2.68)2×0.23

The standard deviation is the square root of the variance:

σ=σ2=1.7176≈1.3106

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