Math Problem Statement

26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 35 college students are randomly selected, find the probability that a. Exactly 10 of them major in STEM. b. At most 11 of them major in STEM. c. At least 7 of them major in STEM. d. Between 7 and 11 (including 7 and 11) of them major in STEM.

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Probability Theory

Formulas

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
P(X ≤ k) = Σ P(X = i) from i=0 to k
P(X ≥ k) = 1 - P(X ≤ k-1)

Theorems

Binomial Theorem

Suitable Grade Level

College level, Probability and Statistics