The Normal Distribution

Question

A variable is normally distributed with mean 22 and standard deviation 3. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed.

a) Find the area to the left of 25. 

b) Find the area to the left of 16. 

c) Find the area to the right of 24. 

d) Find the area to the right of 28. 

e) Find the area between 16 and 29. 

Answer 1

A. P(x<25) = P((25-22)/3) = 0.8913

B. P(x<16) = P((16-22)/3) = 0.0228

C. P(x>24) = P((24-22)/3) = 0.2525

D. P(x>28) = P((28-22)/3) = 0.0228

E. P(16<x<29) = P((29-22)/3) - P((16-22)/3)

= 0.9674

All of the above areas are relative to a total area of 1 under the probability curve, and have been rounded to 4 decimal places.