Question

In a certain distribution of numbers, the mean is 50 with a standard deviation of 6. Use Chebyshev's theorem to tell the probability that a number lies in the indicated interval. Between 35 and 65 O A. At least 15 16 OB 1 At least 25 OC 4 At least 25 OD 21 At least 25

Answer 1

Given that, mean = 50 and standard deviation = 6

According to Chebyshev's theorem, at least (1 - 1/k^{​​​​​​2}) of the data fall within k standard deviations of the mean.

We want to find, the probabilitiy that a number lies between 35 and 65.

For x = 35

k = (35 - 50) / 6 = -15/6 = -2.5

For x = 65

k = (65 - 50) / 6 = 15/6 = 2.5

That means k = 2.5 or 25/10

Therefore,

=1- -2

$= 1 - \frac {1}{(2.5)^2}$

$= 1 - \frac {1}{(\frac {2.5}{10})^2}$

$= 1 - (\frac {10}{25})^2$

$= 1 - \frac {100}{625}$

$= \frac {625-100}{625}$

$= \frac {525}{625}$

$= \frac {21}{25}$

Therefore, the probabilitiy that a number lies between 35 and 65 is at least 21/25

Answer : D)