A z-table is also known as the standard normal distribution table. The probability that a data value is between 28 and 31 is 0.5859.
A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
Given the mean is 26 while the standard deviation is 4. Therefore, the probability that a data value is between 28 and 31 can be written as,
[tex]P(28 < X < 31) = P(\dfrac{28-26}{4} < Z < \dfrac{31-26}{4})[/tex]
[tex]=P(-0.5 < Z < 1.25)\\\\=P(Z < 1.25)-P(Z < -0.5)\\\\= 0.8944- 0.3085\\\\=0.5859[/tex]
Hence, the probability that a data value is between 28 and 31 is 0.5859.
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