Answer:
Probability that the proportion in our sample of red candies will be less than 20% is 0.5 .
Step-by-step explanation:
We are given that 20% of the candy produced are red. A random sample of 100 bags of Skittles is taken.
The distribution we can use here is;
[tex]\frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } }[/tex] ~ N(0,1)
where, p = 0.20 and n = 100
Let [tex]\hat p[/tex] = proportion of red candies in our sample
So, P([tex]\hat p[/tex] < 0.20) = P([tex]\frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } }[/tex] < [tex]\frac{0.20 - 0.20}{\sqrt{\frac{0.2 (1- 0.2)}{100} } }[/tex] ) = P(Z < 0) = 0.5
Therefore, probability that the proportion in our sample of red candies will be less than 20% is 0.5 .
