Question

The time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and standard deviation of 5 minutes. What intervals could you estimate, using the knowledge from this activity, that do not include the mean as a max or min? For example,   is an interval we could estimate. However, it includes the mean as the maximum of the interval. Another example is  as an example of a probability interval that we know from this activity, but it includes the mean as the minimum.

Include at least 7 intervals and their probabilities.

Answer 1

Solution:

Given = 52

= 5

by the empirical formula

+ 1 SD = 68% = 1 = 52 5

2 SD = 95% = 2 = 52 2*5

3 SD = 99.7% = 3 = 52 3*5

7 required intervals and their  probabilities are

1) + 1 SD = 0.68 = P(47<X<57)

2) P(42<X<62) = 0.95

3) P(37<XZ<67) = 0.997

4) P(42<X<47) = 0.135

5) P(57<X<62) = 0.135

6) P(37<X<42) = 0.235

7) P(62<X<67) = 0.235