33% of all college students major in STEM (Science, Technology, Engineering, and Math). If 39 college students are randomly selected, find the probability that a. Exactly 13 of them major in STEM. b. At most 15 of them major in STEM. c. At least 11 of them major in STEM
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
33% of all college students major in STEM (Science, Technology, Engineering, and Math). If 39 college students are randomly selected, find the
a. Exactly 13 of them major in STEM.
b. At most 15 of them major in STEM.
c. At least 11 of them major in STEM.
Given information:
A random sample of college students of size n = 39 is randomly selected.
Percentage of all college students major in STEM (Science, Technology, Engineering, and Math) = 33%, that is,
Probability of success that a randomly selected college student is a major in STEM, p = 0.33
Let X = x represents the number of college students from the sample major in STEM.
Symbolically,
It is required to obtain the probability that:
a. exactly 13 of them major in STEM
b. at most 15 of them major in STEM
c. at least 11 of them major in STEM
Introduction:
The Binomial distribution can be approximated using the normal distribution if:
The mean and the variance of the binomial distribution are computed as np and npq, respectively.
Using the continuity correction factor of 0.5, the various probability expressions are converted as:
Convert the random scores to the corresponding z-scores and obtain the probability values from the z-score table.
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