Question

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories.

a. What is the distribution of X? X ~ N(__________,__________)

b. Find the probability that a randomly selected fat calorie percent is more than 40. Round to 4 decimal places.__________

c. Find the minimum number for the upper quartile of fat calories. Round to 2 decimal places.__________

Answer 1

Solution: Given that mean = 36, sd = 10

a. X ~ N(36,10)

b. P(X > 40) = P((X-mean)/sd > (40-36)/10)
= P(Z > 0.4)
= 1 - P(Z < 0.4)
= 1 - 0.6554
= 0.3446

Use the standard normal table to find the area below 0.4. :

Z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5	0.504	0.508	0.512	0.516	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.5517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.591	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.648	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.67	0.6736	0.6772	0.6808	0.6844	0.6879

c. upper quartile for Z = 0.6745

X = mean + Z*Sd = 36 + (0.6745*10) = 42.745 = 42.75 (rounded)