A study is to be conducted in a hospital to determine the...

A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrative procedures. A sample of 10 nurses is to be selected from a total of the 90 nurses employed by the hospital. a. How many different samples of 10 nurses can be selected? b. Twenty of the 90 nurses are male. If 10 nurses are randomly selected from those employed by the hospital, what is the probability that the sample of ten will include exactly 4 male (and 6 female) nurses?

A study is to be conducted in a hospital to determine the attitudes of nurses toward various administrative procedures. A sample of 10 nurses is to be selected from a total of the 90 nurses employed by the hospital.
a. How many different samples of 10 nurses can be selected?
b. Twenty of the 90 nurses are male. If 10 nurses are randomly selected from those employed by the hospital, what is the probability that the sample of ten will include exactly 4 male (and 6 female) nurses?

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Key Concepts

Combination

A combination is a method for selecting items from a larger pool where the order of selection does not matter. It is calculated using the formula nCr = n! / (r!(n-r)!), which provides the number of ways to choose r items from a total of n items. This concept is fundamental when dealing with problems of sampling without regard to the order of selection.

Binomial Coefficient

The binomial coefficient is the numerical factor that multiplies the successive terms in the binomial theorem. It is also used as the combinatorial term to calculate the number of ways to select a subset of items from a larger set, equivalent to the mathematical representation for combinations. This is crucial in counting problems where specific group sizes are needed.

Hypergeometric Distribution

The hypergeometric distribution is a probability distribution used for sampling without replacement from a finite population. It determines the probability of drawing a specific number of successes (for instance, male nurses) when the total population has a known number of successes and failures. This concept is specifically applicable when calculating probabilities in scenarios where the sample composition is subject to constraints from the population's makeup.

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