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Nataly [62]
3 years ago
11

When Isaac commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 44 minutes and a s

tandard deviation of 5 minutes. Using the empirical rule, determine the interval that represents the middle 95% of his commute times.
Mathematics
1 answer:
mario62 [17]3 years ago
5 0

Answer:

[34,54]

Step-by-step explanation:

-The empirical rule states that the 95% of the sampled observations will fall within two standard deviations of the mean for a normally distributed population.

Where:

  • 68% is the first standard deviation
  • 95% is the second standard deviation about the mean
  • 99.7% is the 3rd standard deviation about the mean.

-Therefore. the middle 95% interval is calculated as:

CI=\mu+2\sigma\\\\=44\pm 2(5)\\\\=44\pm 10\\\\=[34,54]

Hence, the interval is [34,54]

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b)

From the standardized z-score

If [z_i < 2]; it typically implies that the data is unusual

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