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Misha Larkins [42]
3 years ago
11

The time it takes to drive from Orangeville to the Vaughan Mills Mall is normally distributed with a mean of 52 minutes and stan

dard 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.
Mathematics
1 answer:
san4es73 [151]3 years ago
6 0

Given:

Mean of 52 minutes and a standard deviation of 5 minutes.

Solution:

According to the empirical rule: For the normal distribution, all of the data will fall within three standard deviations of the mean.

1: 68% of the data will fall within the first standard deviation from the mean.

2: 95% of the data fall within two standard deviations.

3: 99.7% of the data fall within three standard deviations.

3SD =99.7\%=\mu\pm3\sigma\\

Therefore, the 7 intervals and their probabilities are:

1. 1SD=0.68=P(47

2. 0.95=P(42

3. 0.997=P(37

4.13.5\%=P(42

5.13.5\%=P(57

6. 2.35\%=P(37

7.2.35\%=P(62

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