[Solution] As we have previously noted, a quick approximation is sometimes useful when an exact answer is not required. For a distribution that is symmetric


Question: As we have previously noted, a quick approximation is sometimes useful when an exact answer is not required. For a distribution that is symmetric and bell-shaped (in particular, for a normal distribution), the Empirical Rule states that

- Approximately \(68 \%\) of the data values lie between \(\mu-\sigma\) and \(\mu+\sigma\).

- Approximately \(95 \%\) of the data values lie between \(\mu-2 \sigma\) and \(\mu+2 \sigma\)

- Approximately \(99,7 \%\) of the data values lie between \(\mu-3 \sigma\) and \(\mu+3 \sigma\)

  1. Verify the statements in the Empirical Rule for the normal probability density function with \(\mu=5.3\) and \(\sigma=8.372\)
  2. Estimate \(P(-11.444
  3. Use the normal probability density function to find the probability in part \(b\).

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