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V125BC [204]
3 years ago
6

According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags o

f Skittles, what is the probability that the proportion in our sample of red candies will be less than 20%
Mathematics
1 answer:
igomit [66]3 years ago
5 0

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;

               \frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } } ~ N(0,1)

where, p = 0.20 and n = 100

Let \hat p = proportion of red candies in our sample

So, P(\hat p < 0.20) = P(\frac{\hat p - p}{\sqrt{\frac{\hat p (1- \hat p)}{n} } } < \frac{0.20 - 0.20}{\sqrt{\frac{0.2 (1- 0.2)}{100} } } ) = P(Z < 0) = 0.5

Therefore, probability that the proportion in our sample of red candies will be less than 20% is 0.5 .

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