Question

Return to Example 8.5: Serum cholesterol levels for all males 20 to 35 years old in the United States are approximately normally distributed with a mean of 186 mg/dL and standard deviation of 36 mg/dL.

1. Approximately what percent of all males in the United States between 20 and 35 years old have cholesterol levels between 150 mg/dL and 258 mg/dL? (Report your answer to ONE decimal place.) Hint, displayed below%
2. Approximately what percent of all males in the United States between 20 and 35 years old have cholesterol levels between 186 mg/dL and 294 mg/dL? (Report your answer to TWO decimal places.) Hint, displayed below%

Answer 1

solution

given that

P(150< x <258 ) = P[(150-186 ) / 36< (x - ) / < (258-186 ) /36 )]

= P( -1< Z <2 )

= P(Z <2 ) - P(Z <-1 )

Using z table   

= 0.9772-0.1587

=0.8185

answer=81.9%

(B)

P( 186 < x <294 ) = P[( 186 -186 ) / 36< (x - ) / < (294 -186 ) /36 )]

= P(0< Z <3 )

= P(Z <3 ) - P(Z <0)

Using z table   

= 0.9987-0.5

=0.4987

answer=49.9%