A survey showed that 83 % of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 17 adults are randomly selected, find the probability that at least 16 of them need correction for their eyesight. Is 16 a significantly high number of adults requiring eyesight correction?

Question

Siena Zamora

Mathematics

31 May, 22:21

A survey showed that 83 % of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 17 adults are randomly selected, find the probability that at least 16 of them need correction for their eyesight. Is 16 a significantly high number of adults requiring eyesight correction?

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Hunter Little · Answer 1

18.87%

Step-by-step explanation:

Let's say that adult that needs correction is A (83%) and adult that doesn't need correction is B (17%). There are two combinations of event that result at "at least 16 out of 17 adults chosen need correction" which is:

1. 17A

2. 16A + 1 B

The probability for 17A should be easy to determine, it is simply A^17.

You will need a pascal triangle for 16A + 1 B event combination, not only A^16*B^1. It's pretty easy to know the coefficient since its just 1 different case so it's 16+1 = 17. The chance will be:

1A^17 + 17A^16*B^1=

0.04210 + 0.1466 = 0.1887 = 18.87%

If you use 5% as significant cutoff, then it's not significant because the probability of this occurring is not small.