Question

The National Center for Health Statistics reports that 25% of all Americans between the ages of 65 and 74 have a chronic heart condition. Suppose you live in a state where the environment is conducive to good health and low stress and you believe the conditions in your state promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 25 persons 65 to 74 years of age in your state.

*(Round your answer to 2 decimal places.) **(Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places.) a

. On the basis of the figure from the National Center for Health Statistics, what is the expected number of persons 65 to 74 years of age in your survey who have a chronic heart condition? 6.25

* b. 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 25 if 25% of the population in this age bracket has this health problem?

What do you conclude about your state from the sample data? ** Since the probability is so (high/low), the population of your state may have a (lower/higher) percentage of chronic heart conditions than those of other states.

Answer 1

a)

the expected number of persons 65 to 74 years of age in your survey who have a chronic heart condition

= np = 25*0.25 =6.25

b)

Sample size , n =    25
Probability of an event of interest, p =   0.25

P ( X =    0   ) = C(25,0) * 0.25^0 * (1-0.25)^25 =            0.0007525435

P ( X =    1   ) = C(25,1) * 0.25^1 * (1-0.25)^24 =            0.0062711955

= 0.0007+ 0.0063= 0.0070

c)

Since the probability is so low, the population of your state may have a (lower) percentage of chronic heart conditions than those of other states.

Please revert back in case of any doubt.

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