Suppose x is normally distributed random variable with μ = 12 and σ =2. Find each of the following probabilities.

a. P (x ≥ 13.5) b. P (x ≤ 8) c. P (12.62 ≤ x ≤ 16.54) d. P (7.02 ≤ x ≤ 15.32)

Question

Suppose x is normally distributed random variable with μ = 12 and σ =2. Find each of the following probabilities.

a. P (x ≥ 13.5) b. P (x ≤ 8)   c. P (12.62 ≤ x ≤ 16.54)   d. P (7.02 ≤ x ≤ 15.32)

anonymous · Answer

They just want you to find Z-scores and look up the probabilities in tables. e.g. for the first, find the area to the right of $Z$ where $$Z=\frac{13.5-12}2=\frac{1.5}2=0.75$$You can determine the area to the left and subtract from 1.

anonymous · Answer

(b) just wants the area to the left of $Z=(8-12)/2=-4/2=-2$. Use your table.

For (c) and (d), they want the area between two $Z$:|dw:1370722148193:dw|