please help with question

Question

A survey showed that

80​%

of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If

16 adults are randomly​ selected, find the probability that at least 15 of them need correction for their eyesight. Is

15 a significantly high number of adults requiring eyesight​ correction?

The probability that at least 15 of the 16 adults require eyesight correction is =

​(Round to three decimal places as​ needed.)

Is 15 a significantly high number of adults requiring eyesight​ correction? Note that a small probability is one that is less than 0.05.

Answer 1

use binomial distribution formula

P(n;x,p) probability of x successes in n trials with each trial has probability of success p.

= n!/(n-x)!x! * p^x * (1-p) ^(n-x)

here p = 0.8, n = 16. first determine probability for x = 15, then for x = 16 then add.

if probability is < 0.05, the 15 is a significant number of adults