A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?

Question

Mathematics

Myah Rollins

27 January, 23:51

A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?

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Answers (1)

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Cynthia Harrell · Answer 1

Solution:

To evaluate for P (0.372
z-score is given by:

z = (x-μ) / σ

thus when x=0.372:

z = (0.372-0.4) / 0.028

z=-1

thus

P (x<0.372) = P (z<-1) = 0.1587

when x=0.428

z = (0.428-0.4) / (0.028) = 1

P (x<0.428) = P (z<1) = 0.8413

thus

P (0.372