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------------------------------------------------ A distribution of values is normal with a mean of 240.1 and a standard deviation of 97.5.

Find the probability that a randomly selected value is between −71.9 and 84.1.

To find the probability that a randomly selected value is between -71.9 and 84.1 in a normal distribution with mean of 240.1 and standard deviation of 97.5, we first calculate the z-scores, find their corresponding probabilities in the z-table, and subtract to get the final probability. The answer, in this case, is 0.0541 or 5.41%

Explanation:

The subject of this question is Mathematics, specifically, it's about Probability within a Normal Distribution. To answer this, we will have to standardize the numbers and use the Z-table to find the probabilities.

Calculate the z-scores for each divisors. The z-score is the number of standard deviations a particular X is from the mean. Use the formula z = (X - μ) / σ. For -71.9, z1 = (-71.9 - 240.1) / 97.5 = -3.20 and for 84.1, z2 = (84.1 - 240.1) / 97.5 = -1.60.
Refer to Z-table to calculate probabilities for the z-scores. Approx, the values are 0.0007 for -3.20 and 0.0548 for -1.60.
The probability that X is between -71.9 and 84.1 is P(-3.20 < Z < -1.60) which is equal to P(Z < -1.60) - P(Z < -3.20) = 0.0548 - 0.0007 = 0.0541 or 5.41%.

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