Complete question :
A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnell is a middle school student with a height of 161.4 centimeters.
What proportion of student heights are lower than Darnell's height?
Answer:
0.716 (71.6%)
Step-by-step explanation:
Given that :
Mean, μ = 150
Standard deviation, σ = 20
Darnell's height, x = 161.4
(x < 161.4)
We obtain the standardized score, then find the proportion using a standard normal distribution ;
Zscore = (x - μ) / σ
Zscore = (161.4 - 150) / 20
Zscore = 11.4 / 20
Z = 0.57
P(Z < 0.57) = 0.71566 (Z probability calculator)
This means that about 0.716 (0.716 * 100% = 71.6%) of student's height are lower than 161.4 centimeters
