Question
Asked Feb 9, 2020
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Assume that 28% of randomly selected adults have high cholesterol (with a level of at least 240mg/dl. or are taking medicine to reduce cholesterol). Based on results from the National Center for Health Statistics. Assume that a group of five adults is randomly selected. If the group of five adults includes exactly 1 with high cholesterol, is that value of 1 significantly low?

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Expert Answer

Step 1

Binomial distribution:

The binomial distribution gives the probability of number of successes out of n trials in a series of Bernoulli trials. The probability mass function (pmf) of a binomial random variable x is given as:

Statistics homework question answer, step 1, image 1

Step 2

Define the random variable x as the number of adults having high cholesterol. Here, the number of adults chosen (n) is 5 and each of them is independent of the other. Also, there are two possible outcomes (having cholesterol or not having cholesterol) and the probability that an adult will have cholesterol (p) is 0.28. Thus, x follows a binomial distribution.

Substitute x as 1, n as 5, p as 0.28 and q as 0.72 (=1-0.28).

By applying the binomial distribution,

 

Statistics homework question answer, step 2, image 1

Step 3

Range rule of thumb:

The range rule of thumb is as follows:

  • The values are significantly low if they are less than or equal to (µ-2σ).
  • The values are significantly high if they are greater than or equal to (µ+2σ).
  • The values are not significant if they are between (µ-2σ) and (µ+2σ).

Th...

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