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ruslelena [56]
3 years ago
15

At a restaurant, 25% of the dinner plates are clean. There are 80 total dinner

Mathematics
1 answer:
pochemuha3 years ago
7 0

Answer:

20

Step-by-step explanation:

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during a particular period a university's information technology office received 20 service orders for problems with printers, o
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Answer:

0.2384 = 23.84% probability that 3 were laser printers.

Step-by-step explanation:

The printers will be chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

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

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In this question:

20 orders means that N = 8

8 were laser printers, which means that k = 8

Sample of 5 means that n = 5

What is the probability that 3 were laser printers?

This is P(X = 3).

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

P(X = 3) = h(3,20,5,8) = \frac{C_{8,3}*C_{12,2}}{C_{20,5}} = 0.2384

0.2384 = 23.84% probability that 3 were laser printers.

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