Question

A population of values has a normal distribution with μ=152.8 and σ=26.2 . You intend to draw a random sample of size n=94 . Find the probability that a single randomly selected value is less than 149.6. P(X < 149.6) =

Answer 1

P(x < 149.6) = 0.11821

Explanation:

We start by calculating the z-score of the parameter given

Mathematically,

z-score = (x-mean)/SD/√n

z-score = (149.6-152.8)/26.2/√94

z-score = -3.2/2.70

z-score = -1.18

So the probability we want to calculate is;

P( x < -1.18)

we can use the standard normal distribution table to get this

From the standard normal distribution table, this value is 0.11821