Question

X is a normally distributed random variable with mean 43 and standard deviation 14.

What is the probability that X is between 1 and 85?
Use the 0.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

Answer 1

Notice that

85 = 43 + 3•14

1 = 43 - 3•14

so that if
`1 \le X \le 85`, then
`X` is within 3 standard deviations of the mean. The given rule then says

`\mathrm{Pr}(1 \le X \le 85) \approx \boxed{0.997}`