Question

Based on experience, Farmer Fern knows that 15% of her eggs will be damaged in

route to the stores. In a sample of 100 eggs, what is the probability that less than
13% will be damaged?

Answer 1

Answer: 0.2877

Explanation:

Given : The proportion of eggs will be damaged in route to the stores = 15% = 0.15

Sample size = 100

Let p be the probability of her eggs will be damaged.

The probability that less than 13% will be damaged is given by :-

`P(p<0.13)=P(\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}<\frac{0.13-0.15}{\sqrt{(0.15*(1-0.15))/(100)}})`

`=P(z<-0.56)`

`=1-P(z<0.56)\\\\= 1-0.7123\\\\= 0.2877`

Hence, the required probability = 0.2877