Question

1) According to the Centers for Disease Control and Prevention (CDC), the mean total cholesterol level for persons 20 years of age and older in the United States from 2007–2010 was 197 mg/dL. a. What is the probability that a randomly selected adult from the population will have a total cholesterol level of less than 183 mg/dL? Use a standard deviation of 35 mg/dL and assume that the cholesterol levels for the population are normally distributed. b. What is the probability that a randomly selected sample of 150 adults from the population will have a mean total cholesterol level of less than 183 mg/dL? Use a standard deviation of 35 mg/dL.

Answer 1

Solution :

Given that ,

mean = = 197 mg/dl

standard deviation = = 35 mg/dl

a) P(x < 183)

= P[(x - ) / < (183 - 197) / 35]

= P(z < -0.40 )

Using z table,

= 0.3446

b) n = 150

= = 197 mg/dl

= / n = 35/ 150 = 2.86

P( < ) = P(( - ) / < (183 - 197) / 2.86)

= P(z < -4.90)

Using z table

= 0