High School

Recovery time for an illness follows a normal distribution with a mean of 12.4 days and a standard deviation of 2.1 days. Use the 68-95-99.7 Rule to answer the following questions.

Answer :

Final answer:

To find the probability of a diagnosis occurring between 1.75 and 1.85 days, we can use z-scores and the standard normal distribution.

Explanation:

To find the probability that a diagnosis occurs on average between 1.75 and 1.85 days, we need to standardize the values using the formula z = (x - mean) / standard deviation. The z-scores are calculated as follows:

  • z1 = (1.75 - 12.4) / 2.1 = -5.1905
  • z2 = (1.85 - 12.4) / 2.1 = -4.5238

Then, we can use a standard normal distribution table or calculator to find the probability between these z-scores.

Learn more about Normal distribution here:

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