Question

A survey showed that 84% of adults need correction eyeglasses, contacts, surgery, etc.) for their eyesight lf 9 adults are randomly selected find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction?
The probability that no more than 1 of the 9 adults require eyesight correction is _____ (Round to three decimal places as needed.)

Is 1 a significantly low number of adults requiring eyesight correction? Note that a small probability is one that is less than 0.05

A. No, because the probability of this occurring is small.
B. No, because the probability of this occurring is not small.

C. Yes, because the probability of this occurring is small.
D. Yes, because the probability of this occurring is not small.

Answer 1

Solution:

Given: A survey showed that 84% of adults need correction eyeglasses, contacts, surgery, etc.) for their eyesight

thus p = 0.84

9 adults are randomly selected

thus n = 9

Since number of adults are randomly selected and are independent with probability of success = probability of adults need correction for their eyesight is constant for each adults, thus:

x = Number of adults need correction for their eyesight follows a Binomial distribution with parameters n = 9 and p= 0.84

Part a) Find

P( no more than 1 of the 9 adults require eyesight correction ) =............?

that is find:

Binomial probability formula :

Where q = 1 – p = 1 - 0.84 = 0.16

thus

and

thus

Part b) Is 1 a significantly low number of adults requiring eyesight correction?

Since P(X =1) is approximately = 0 and < 0.05, so 1 is a significantly low number of adults requiring eyesight correction

C. Yes, because the probability of this occurring is small.