Answer :
The standard deviation of the heights is 1.561 based on the given information.
What is Z -score?
A Z-score is defined as the fractional representation of data point to the mean using standard deviations.
The z-score which separates the top 10% of a normally distributed
the population is 1.282.
The formula of the z-score is represented as:
z = (x - μ)/sd
As per the question, we have x = 40 and μ = 38
1.282 = (40-38)/sd
sd = 2/1.282
sd = 1/0.641
Apply the division operation, and we get
sd = 1.561
Thus, the standard deviation will be 1.561.
Learn more about the standard deviation here:
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