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

Answer:

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 .

Step-by-step 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 .