X is normally distributed with mean 50 and standard deviation 8. What value of X is such that only 8% of values are below it?
Mean = 50
Standard deviation = 8
p-value = 8% or 0.08
Firstly needs to find Z value using p-value from normal distribution table.
The value of X is such that only 8% of values are below mean, so p-value is:
= 1 - 0.08 = 0.92
Then the standardize value is:
Z = -1.41
"Z=\\frac{\\mu-x}{\\sigma}"
"-1.41=\\frac{x-50}{8}"
"x-50=-1.41\\times8"
"x=-11.28+50=38.72"
This means approximately 8% of values are below the mean.
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