Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth.

Question

Mathematics

Marcella

31 July, 02:26

Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth.

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Answers (2)

Know the Answer?

Herman · Answer 1

C.) 0.213

Step-by-step explanation:

Took the test on Ed.

Gordon Todd · Answer 2

0.213

Step-by-step explanation:

This is a probability question.

Let c = probability of a student taking chemistry. That is 40% = 4/10

Now, let d be the probability of a student not taking chemistry, that would be 60% = 6/10

Now out of 12 sampled, we want to calculate the probability that exactly 4 have taken chemistry.

The easiest approach here is by the use of bernoulli approximation.

Thus,

P (x = 4) = 12C4 * c^4 * d^8

P (x = 4) = 12C4 * (0.4) ^4 * (0.6) ^8

P (x = 4) = 495 * 0.0256 * 0.01679616

P (x = 4) = 0.2128

To the nearest thousandth, the probability is 0.213