Question

You test your grade 12 maths cohort with a standardised test which has an average pass rate of 80%. There are 120 students in the cohort. What is the probability that less than 100 students pass?

The answer is (0.82), please explain how [show working].

Answer 1

We have given

p=0.80

n=120

we have to find

p(X<100)

Here we will use normal approximation(beacsuse n>30, n*p=96>10 and n*(1-p)=24>10)

X~Normal(mean=n*p=120*0.8=96,SD=sqrt(n*p*(1-p)) =SQRT(120*0.8*0.2)=4.38178)

p(X<100)=p((X-mean)/SD<(100-96)/4.38178)

=p(Z<0.912871)

using excel

p(Z<0.912871)=NORM.DIST(B2,0,1,1)=0.8193=0.82

p(X<100)=0.82

Answer:

the probability that less than 100 students pass =0.82

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