Question

In a study of helicopter usage and patient survival, among the 56,074 patients transported by helicopter, 235 of them

Answer 1

Using the hypergeometric distribution, it is found that the probability is 0.845 = 84.5%.

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• The patients are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

The parameters are:

• x is the number of successes.
• N is the size of the population.
• n is the size of the sample.
• k is the total number of desired outcomes.

Combination formula:

is the number of different combinations of x objects from a set of n elements, given as:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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• 56074 patients, thus $N = 56074$
• Sample of 40, thus, $n = 40$
• 235 left against medical advice, thus, $k = 235$.

The probability that none left against medical advice is P(X = 0), so:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,56074,40,235) = \frac{C_{235,0}*C_{55839,40}}{C_{56074,40}} = 0.845$

The probability is 0.845 = 84.5%.

A similar problem is given at brainly.com/question/24008577