Question

Use the 68-95-99.7 rule to approximate what proportion of observations in N(70,5) distribution fall between 70 and 80. (Show your answer in percentage.)

Answer 1

Here, $X\sim N(70,5)$

We know that according to the 68-95-99.7 rule, approximately 68%, 95%, 99.7% observations for a bell shaped distribution lie within 1, 2 and 3 standard deviations from the mean respectively.

Now, 95% observations lie in the interval:

$(\mu-2\sigma,\mu+2\sigma)=(70-2(5),70+2(5))=(60,80)$

Since the distribution is symmetric, so percentage of observations lying between 70 and 80 is given by:

95 - 47.5%。 2