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 and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
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
In this problem, we have that:
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?
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%.