Question

A quantitative data set has mean 23 and standard deviation 2. At least what percentage of the observations lie between 15 and 31​? At least nothing​% of the observations lie between 15 and 31.

Answer 1

Answer:

Atleast 93.75% of data lies between 15 and 31​.

Step-by-step explanation:

We are given the following in the question:

Mean = 23

Standard deviation = 2

We have to find he data lying between 15 and 31.

$15 = 23 - 4(2) = \mu - 4\sigma\\31 = 23 + 4(2) = \mu + 4\sigma$

Thus, we have to find the data lying within 4 standard deviation from the mean.

Chebyshev's Theorem:

• According to this theorem atleast  $1 - \dfrac{1}{k^2}$  percent of data lies within k standard deviation of mean.
• For k = 4.

$1 - \dfrac{1}{(4)^2} = 0.9375 = 93.75\%$

Thus, atleast 93.75% of data lies between 15 and 31​.