13% of people took a math course. What is the probability that in a 350 randomly selected sample, less than 40 people take the course?

Jadon Melendez

Jadon Melendez

Answered question

2022-07-22

13 % of people took a math course. What is the probability that in a 350 randomly selected sample, less than 40 people take the course?

So I have X B i n ( 350 , 13 100 )
Then let Y N ( 13 100 , 0.00032314 2 )
I want P ( X < 40 ) = P ( p ^ < 4 10 )
Then P ( z < 4 10 13 100 0.00032314 2 ) which is obviously very wrong.
Where did it go wrong, and why did it go wrong?

Answer & Explanation

Octavio Barr

Octavio Barr

Beginner2022-07-23Added 11 answers

The number X of people taking the course is B ( n , p )-distributed with n = 350 , p = 0.13. Its variance is npq, n p q , q := 1 p. The z-score of X is Z := X n p n p q , so the Normal approximation of P ( X < 40 ) is
P ( Z < 40 n p n p q ) = P ( Z < 40 350 × 0.13 350 × 0.13 × 0.87 ) .
(Depending on how you seek to discretize the Normal variable approximating X, you might replace 40 with e.g. 39.5.)

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