Question

A random variable X has a normal distribution with mean 50 and variance of 10. Find the range of scores that lie:

A.Within one standard deviation from the mean.

B.Within two standard deviation from the mean.

Answer 1

Mean: $\mu=50;$

variance: $\sigma^2=10;$

standard deviation: $\sigma=\sqrt{10} \approx3.16.$

A. The range of scores that lie within one standard deviation from the mean:

$(\mu-\sigma, \mu+\sigma) =(50-3.16, 50+3.16)=$

$=(46.84, 53.16).$

B. The range of scores that lie within two standard deviations from the mean:

$(\mu-2\sigma, \mu+2\sigma) =(50-2\cdot3.16, 50+2\cdot3.16)=$

$=(43.68, 56.32).$