Answer to Question #323987 in Statistics and Probability for deaho

Question

A random variable X has a normal distribution with mean 45 and variance of 9.

Find the range of scores that lie:

a. within one standard deviation from the mean

b. within two standard deviations from the mean

Answer 1

$\text{The mean }\mu=45,\text{the standard deviation }\sigma=\sqrt{9}=3.$

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

$(\mu-\sigma,\mu +\sigma)=(45-3,45+3)=(42,48).$

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

$(\mu-2\sigma,\mu +2\sigma)=(45-2\cdot3,45+2\cdot3)=(39,51).$