The figure shows a normal N(400, 23) distribution. Find the x value for the shaded area. C.2 we get P(z

Question

The figure shows a normal N(400, 23) distribution. Find the x value for the shaded area.  C.2 we get P(z < -1.645) = .05, so x = µ + zσ = 400 - 1.645(23) = 362.2, or from Excel =NORM.INV(0.05,400,23) = 362.2.
A)379.1 
B)362.2 
C)355.7 
D)347.6

Quizplus · Accepted Answer

We need to find the x value for the shaded area which represents a probability of 0.05 in the left tail of the distribution. Using the z-table lookup, we find the z-score corresponding to the probability of 0.05 to be -1.645. We can then use the formula x = µ + zσ where µ is the mean (400), σ is the standard deviation (23), and z is the z-score (-1.645) to find the corresponding x value. Simplifying the formula, we get x = 400 - 1.645(23) = 362.2. Therefore, the best choice is B.

The Figure Shows a Normal N(400, 23) Distribution