If x is normally distributed with mean 12 and standard deviation 2,then P(x ≤ 9)is
A)P(z ≤ 9/10).
B)P(z ≤ −3/2)
C)P(z ≤ 2/3)
D)P(z ≤ −3/4)

Question

Quizplus · Accepted Answer

We need to transform x into a standard normal variable using z = (x-μ)/σ, where μ is the mean and σ is the standard deviation. 
z = (9-12)/2 = -1.5 
Therefore, we need to find P(z ≤ -3/2) which is equivalent to the probability of the left tail of the standard normal distribution. Using a standard normal table or calculator, we get P(z ≤ -1.5) ≈ 0.0668.

If X Is Normally Distributed with Mean 12 and Standard