Question

There is a 40% probability that a student PASSES their first statistics exam. Using a Binomial Distribution, if we randomly select 7 students: What is the probability that more than 5 PASS their first statistics exam

Answer 1

The probability that more than 5 students will pass their exam is 0.0188416.

How to find the probability?

The probability that a student passes their examination = 40% = 0.4

The probability that more than 5 students pass their statistics exam = Probability that 6 students pass their exam + Probability that 7 students pass their exam

The probability that 6 students pass their exam =

$7C_{6} (0.4)^{6} (0.6)^{1}\\=7(0.4)^6(0.6)\\=0.0172032$

The probability that 7 students pass their exam =

$7C_{7} (0.4)^{7} (0.6)^{0}\\=(0.4)^7\\=0.0016384$

The probability that more than 5 students pass their statistics exam = 0.0172032 + 0.0016384

= 0.0188416

Therefore, we have found the probability that more than 5 students will pass their exam to be 0.0188416.

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