Question

1. According to the US National Center for Health Statistics, the distribution of cholesterol levels in teenage boys is approximately normally distributed with a mean of 170, and a standard deviation of 30. Levels above 200 need attention. Find the probability that a teenage boy has a cholesterol level:

   1. Greater than 200.

   2. Less than 120.

Answer 1

Solution :

Given that,

mean = = 170

standard deviation = = 30

a ) P (x > 200 )

= 1 - P (x < 200 )

= 1 - P ( x -  / ) < ( 200 - 170 / 30 )

= 1 - P ( z < 30 / 30 )

= 1 - P ( z < 1 )

Using z table

= 1 -0.8413

= 0.1587

Probability = 0.1587

b ) P( x < 120 )

P ( x - / ) < ( 120 - 170 / 30 )

P ( z < -50 / 30 )

P ( z < -1.67 )

= 0.0475

Probability = 0.0475