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Strike441 [17]
3 years ago
5

According to a candy​ company, packages of a certain candy contain 1616​% orange candies. Suppose we examine 100100 random candi

es. a. What value should we expect for our sample percentage of orange​ candies? b. What is the standard​ error? c. Use your answers to fill in the blanks below. We expect​ ____% orange​ candies, give or take​ _____%.
Mathematics
1 answer:
GaryK [48]3 years ago
3 0

Answer:

a) By the Central Limit Theorem, 16%.

b) 0.0367 = 3.67%

c) We expect 16% orange​ candies, give or take 3.67%.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For samples of size n of a proportion p, the expected sample percentage is p and the standard error is s = \sqrt{\frac{p(1-p)}{n}}

In this problem, we have that:

p = 0.16, n = 100

a. What value should we expect for our sample percentage of orange​ candies?

By the Central Limit Theorem, 16%.

b. What is the standard​ error?

s = \sqrt{\frac{0.16*0.84}{100}} = 0.0367

0.0367 = 3.67%

c. Use your answers to fill in the blanks below. We expect​ ____% orange​ candies, give or take​ _____%.

We expect 16% orange​ candies, give or take 3.67%.

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