Question

If ? is a random variable that follows a normal distribution with a mean of 20 and standard deviation 3.2, what value of ? represents the 50th percentile?

Answer 1

Solution :

mean = $\mu$ = 20

standard deviation = $\sigma$ = 3.2

Using standard normal table,

P(Z < z) = 50% = 0.50

P(Z < 0) = 0.50

z = 0

Using z-score formula,

Y= z * $\sigma$ + $\mu$

Y = 0 * 3.2 + 20 = 20

50th percentile =20