Question

A survey showed that 77​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 22 adults are randomly​ selected, find the probability that no more than more than 11 of them need correction for their eyesight. Is 11 a significantly low low number of adults requiring eyesight​ correction?

Answer 1

The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight​ correction .

Explanation:

A survey showed that 77​% of adults need correction for their eyesight.

If 22 adults are randomly​ selected, find the probability that no more than more than 11 of them need correction for their eyesight.

n =22

p = 0.77

q = 1-p = 1- 0.77=0.23

We are supposed to find
`P(x\leq 11)`

`P(x\leq 11)=P(x=1)+P(x=2)+P(x=3)+.....+P(x=11)`

Formula :
`P(x=r)=^nC_r p^r q^(n-r)`

`P(x\leq 11)=^(22)C_1 (0.77)^1 (0.23)^(22-1)+^(22)C_2 (0.77)^2 (0.23)^(22-2)+^(22)C_3 (0.77)^1 (0.23)^(22-3)+.....+^(22)C_(11) (0.77)^1 (0.23)^(22-11)`

Using calculator

`P(x\leq 11)=0.00512`

So, The probability that no more than more than 11 of them need correction for their eyesight is 0.00512

No, 11 is not a significantly low low number of adults requiring eyesight​ correction .