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.

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Elias Melendez · Accepted Answer

Final Answer : False, Explanation :   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 = X − μ σ Z = \frac{X - \mu}{\sigma} Z = σ X − μ ​  , where   X X X   is the value for which we're finding the Z-score,   μ \mu μ   is the mean, and   σ \sigma σ   is the standard deviation. For   X = 75 X = 75 X = 75   and   X = 90 X = 90 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.

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