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An administrator surveys a random sample of 48 out of 900 middle school
students. Using the survey results, the administrator estimates that 225 students
are in favor of the new dress code. How many of the 48 students surveyed were
in favor of the new dress code?

Respuesta :

CintiaSalazar

Considering the definition of probability, 12 of the 48 students surveyed were in favor of the new dress code.

Definition of probability

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)=number of favorable events÷ number of total events

Probability that students are in favor of the new dress code

In this case, you know:

  • Total number of middle school students = 900 (number of possible cases)
  • The number of students are in favor of the new dress code = 225 (number of favorable cases)

Replacing in the definition of probability:

P(A)=225 students÷ 900 students

Solving:

P(A)= 0.25

Expressed as a percentage:

P(A)= 25%

Number of the 48 students surveyed were that in favor of the new dress code

In this case, you know:

  • Total number of middle school students = 48 (number of possible cases)
  • 25% students are in favor of the new dress code (P(A)= 25%= 0.25)

Replacing in the definition of probability:

0.25=students in favor of the new dress code÷ 48 students

Solving:

students in favor of the new dress code= 0.25×48 students

students in favor of the new dress code= 12 students

Finally, 12 of the 48 students surveyed were in favor of the new dress code.

Learn more about probability:

brainly.com/question/3283947

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