Calculating Mean and Standard Deviation

Question

Two children in the same age group have a doctor's appointment. Child 1 has a weight of 32.1875 lbs and falls at the 39th percentile. Child 2 has a weight of 32.85 lbs and places them at the 46th percentile. The weight of these children follows a normal distribution. What are the mean and standard deviation?

Answer 1

z = (x - mean)/standard deviation

39th percentile has z of -0.28

46th percentile has z of -0.1

-0.28 = (32.1875 - mean)/standard deviation

-0.1 = (32.85 - mean)/standard deviation

we have two equations and two unknowns

for ease of computation let x = mean y = standard deviation

-0.28 = (32.1875 - x)/y

-0.1 = (32.85 - x)/y

-0.28y = 32.1875 - x

-0.1y = 32.85 - x

x - 0.28y = 32.1875

x - 0.1y = 32.85

subtract 2nd equation from 1st

-0.18y = -0.6625

y = 3.68

substitute value of y in second equation and solve for x:

x - (0.1)(3.68) = 32.85

x = 33.218

mean is 33.218 and standard deviation is 3.68