The time it takes a student to finish a final exam test is known to be normally distributed with a mean equal to 84 minutes with a standard deviation equal to 10 minutes. Given this information, the probability that it will take a randomly selected student between 75 and 90 minutes is approximately .0902.

Question

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To find the probability that it will take a randomly selected student between 75 and 90 minutes to finish the exam, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value for which we're finding the Z-score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $X = 75$ and $X = 90$, we calculate the Z-scores and then use the standard normal distribution table or a calculator to find the probabilities corresponding to these Z-scores. The actual probability is not .0902; it is calculated based on the area under the normal curve between the Z-scores for 75 and 90 minutes. This area represents the probability sought and is typically larger than .0902 for the given parameters.

The Time It Takes a Student to Finish a Final