25% of all Canadians between the ages of 65 and 74 have a chronic heart conditio

Question

25% of all Canadians between the ages of 65 and 74 have a chronic heart condition. Suppose you believe the conditions in your province promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 20 persons 65 to 74 years of age in your province. (USE EXCEL FORMULAS)

a.What is the probability that fewer than 5 of them have a chronic heart condition?

b.On the basis of the figure from the National Center for Health Statistics, what is the expected number of persons in your survey who have a chronic heart condition?

c.What is the most likely number of people (in a sample of 20) without chronic heart condition?

d.Suppose only one person in your survey has a chronic heart condition. What is the probability of getting one or fewer people with a chronic heart condition in a sample of 20?

e.What can you conclude about your province?

Explanation / Answer

Solution:-

p = 0.25

a) The probability that fewer than 5 of them have a chronic heart condition is 0.4148.

x = 5

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 5) = 0.4148.

b) The expected number of persons in your survey who have a chronic heart condition is 5.

E(x) = n × p

E(x) = 20 × 0.25

E(x) = 5

c) The most likely number of people without chronic heart condition is 15.

d) The probability of getting one or fewer people with a chronic heart condition in a sample of 20 is 0.0243.

x = 1

By applying binomial distribution

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 1) = 0.0243.

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