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StatisticsQ&A LibraryAssume 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?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?

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:

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,

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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