Find the indicated probability.

Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

𝜇 = 22; 𝜎 = 3.8

P(x ≥ 30) =

Answer 1

I will try to explain this shortly. Firstly, we need to use z scores for this( I am assuming you know the formula)

Z=(X-M)/σ

Z=(30-22)/3.8

Z=2.105 ( we need to check the Z-Score table or use your calculator)

P(Z≤2.105)≅ 0.9829

P(Z>2.105)≅ 1-0.9829≅ 0.02

That means roughly 2%=P(x ≥ 30)

Answer 2

transform x to z statistic with standard normal distribution (mean 0 standard deviation 1) using

z = (x - mean)/SD, where x = 30, mean = 22 and SD = 3.8

z = (30 - 22)/3.8 = 2.11

P(x >= 30) = P(z > 2.11) = 1 - P(z < 2.11) = 1 - 0.9826 = 0.0174