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Assume that 30% of students at a university wear contact lenses.
a) We randomly pick 100 students. Let
represent the proportion of students in this sample who wear contacts. What’s the appropriate model for the distribution of
Specify the name of the distribution, the mean, and the standard deviation. Be sure to verify that the conditions are met.
b) What’s the approximate probability that more than one-third of this sample wears contacts?
A) To check if we can apply the Central Limit Theorem in a particular experiment, we have to check the following conditions: Independence assumption, randomization condition, 10% condition, and Large Enough sample condition.
Given that p = 0.30 is the percentage of students in the university that has contact lenses and n = 100 which is the number of samples we got, the experiment is checked using these conditions:
B) In getting the probability of the getting more than 1/3 who wears contact tenses in the sample, we use the normal distribution stated at (16a) and standardize it, such that,