The probability that a data value is between 54 and 66 is 81.9%
z score is used to determine by how many standard deviations the raw score is above or below the mean.
The z score is given by:
[tex]z = \frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]
Given that μ = 62, σ = 4
For x = 54:
[tex]z=\frac{54-62}{4}=-2[/tex]
For x = 66:
[tex]z=\frac{66-62}{4}=1[/tex]
P(54 < x < 66) = P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 81.9%
The probability that a data value is between 54 and 66 is 81.9%
Find out more on z score at: brainly.com/question/25638875
