A survey showed that 76% of adults need correction...

A survey showed that 76% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 14 adults are randomly selected, find the probability that at least 13 of them need correction for their eyesight. Is 13 a significantly high number of adults requiring eyesight correction? The probability that at least 13 of the 14 adults require eyesight correction is . (Round to three decimal places as needed.)

Transcript

00:01 Okay, in this problem, we have a survey that showed that 76 % of adults need correction, like eyeglasses, contact, surgery, etc., for their eyesight.

00:11 So 76%, that is another way of saying 0 .76 as the proportion.

00:20 Okay, if we keep going, we have 14 adults.

00:23 They're randomly selected, and we want to find the probability that at least 13 of them need correction for their eyesight.

00:31 Okay, so 14 adults were given.

00:33 So that means our sample size or n is 14.

00:36 Now, whenever you have the proportion, 0 .76, you also have its complement, which is also represented with the letter q.

00:44 So if you do 1 minus that proportion or 1 minus p or 1 minus 0 .76, you will find its complement or q, which is 0 .24.

00:55 Basically the percent of adults that do not need correction.

00:59 Okay, great.

01:00 So it says we want to find a probability that at least, 13 of them need, at least 13 of the 14 adults require some sort of eyesight correction.

01:10 So what we're trying to do is we're trying to find the probability that x is greater than or equal to 13.

01:18 At least 13 means 13 or more.

01:22 So greater than or equal to 13.

01:25 So we're going to use a binomial distribution to use these values to compute this probability.

01:32 Okay.

01:35 So, the binomial distribution formula.

01:38 I'm going to go ahead and just write it here that we're going to use it.

01:54 Okay, so here is our binomial distribution formula.

01:57 So what we're going to do is we're going to take the values that we have and we're going to plug them in.

02:05 Okay, so since we're doing the probability of selecting someone and having a probability of at least 13 out of the 14 adults require eyesight correction, in order to do this, we're going to have, doing a binomial distribution.

02:19 One one we can do this is we want to find the probability, of exactly 13, needing some sort of eyesight correction.

02:27 And we want to find the probability of exactly 14, having some sort of eyesight correction.

02:32 Then we can add that probably together to find the probability of at least 13...

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