Question

Problem B:

 Cholesterol is a fatty substance that is an important part of the outer lining (membrane) of cells in the body of animals. Its normal range for an adult is 120-240 mg/dl. The Food and Nutrition Institute of the Philippines found that the cholesterol level for Filipino adult has a mean of 159.2 mg/dl and 83.4% of adults have a cholesterol level below 200 mg/dl. Suppose that the cholesterol level is normally distributed. 

e) An adult is thought to be at high risk if his/her cholesterol level is more than two standarod

 f) If a randomly selected adult is not at high risk, what is the probability that he/she is at 

g) What percentile is the cholesterol level of 210 mg/dl? Also provide the name of the 

h) A random sample of 18 adults is selected. Find the probability that more than 16 people irn risk according to this criterion? deviations above the mean. What percentage of the population is at high risk? moderate risk? percentile ( th percentile) and χα notation with numerical value of α. the sample have cholesterol level below 210 mg/dl

Answer 1

Answer to the question)

Part e)

We use empirical formula here

95% of the people lies within 2 standard deviations, and hence only 5% of the people fall beyond 2 standard deviations. Half of them are on the left hand side and half of them are on the right hand side. Thus only 2.5% of the people on the right hand side are the people with high risk of cholesterol

.

Part f)

The proportion of people between 1 standard deviation and 2 standard deviations is a sfollows:

Proportion of people within 1 standard deviation = 68/2 = 34%

Proportion of people within 2 standard deviations = 95% / 2 = 47.5%

Proportion or percent in between = 47.5 -34 = 13.5%.

In probabilistic terms = 0.1350

.

Part g)

Standard deviation = 42.062

Mean = 159.2

X = 210

Z = (x – M ) / SD

Z = (210-159.2) / 42.062

Z = 1.21

Percentile = 0.8869 or 88^th percentile

.

Part h)

P(x>16) = P(x=17) + P(x=18)

P(x=17) = 18C17 * 0.8869^17 * 0.1131^1 =0.2646

[binomial probability formula, n = 18 . x= 17, p = 0.8869]

[formula P(x=x) = nCx * p^x * (1-p)^(n-x)]

P(x=18) = 18c18 * 0.8869^18 =0.1152

P(x>16) = 0.2646 +0.1152 = 0.3798