Question

A data set has a mean of 1500 and a standard deviation of
100.

**
a.** Using Chebyshev's theorem, what percentage of the
observations fall between 1300 and 1700?

**
b.** Using Chebyshev’s theorem, what percentage of the
observations fall between 1200 and 1800?

Answer #1

Solution:

Given, the distribution have

mean = 1500 and SD = 100

According to Chebyshevs Theorem ,

P[( - k) < X < ( + k) ] =

a)

1300 = 1500 - (2 * 100) = - 2

1700 = 1500 + (2 * 100) = + 2

So , here k = 2

= 1 - (1/2^{2} ) = 0.75 = 75%

Answer : **75%**

b)

Here . k = 3

= 1 - (1/3^{2} ) = 0.89 = 89%

Answer: **89%**

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