Using the normal distribution, it is found that there is a 62.4% probability that a data value is between 37 and 41.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
As a proportion, the probability that a data value is between 37 and 41 is the <u>p-value of Z when X = 41 subtracted by the p-value of Z when X = 37</u>, hence:
X = 41:
Z = 1.5
Z = 1.5 has a p-value of 0.933.
X = 37:
Z = -0.5
Z = -0.5 has a p-value of 0.309.
0.933 - 0.309 = 0.624,
0.624 = 62.4% probability that a data value is between 37 and 41.
More can be learned about the normal distribution at brainly.com/question/24663213
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