Question

In a recently released report, the total blood cholesterol levels for adult Americans is an average of 191 mg/dL with a standard deviation of 11.8 mg/dL.

13. Find the percentage of the population with a cholesterol reading of less

         than 190 mg/dL.

14. Find the percentage of the population with a cholesterol reading of more

         than 195 mg/dL.

15. Find the percentage of the population with a cholesterol reading between

185 and 195 mg/dL.

16. Find the percentage of the population with a cholesterol reading less than

186 mg/dL or greater than 196 mg/dL.

Answer 1

#13.
P(X <= 190) = P(z <= (190 - 191)/11.8)
= P(z <= -0.08)
= 0.4681

#14.
P(X >= 195) = P(z <= (195 - 191)/11.8)
= P(z >= 0.34)
= 1 - 0.6331
= 0.3669

#15.
P(185 <= X <= 195) = P((195 - 191)/11.8) <= z <= (195 - 191)/11.8)
= P(-0.51 <= z <= 0.34) = P(z <= 0.34) - P(z <= -0.51)
= 0.6331 - 0.305
= 0.3281

#16.
P(186 <= X <= 196) = P((196 - 191)/11.8) <= z <= (196 - 191)/11.8)
= P(-0.42 <= z <= 0.42) = P(z <= 0.42) - P(z <= -0.42)
= 0.6628 - 0.3372
= 0.3256

required probability = 1 - 0.3256 = 0.6744