Math Problem Statement

Consider a binomial experiment with N=20 and P=0.70.

a. Compute F(12) (to 4 decimals).

b. Compute F(16) (to 4 decimals).

c. Compute P(X≥16) (to 4 decimals).

d. Compute P(X ≤15)(to 4 decimals).

e. Compute E(X) .

f. Compute VAR(X) (to 1 decimal) and ? (to 2 decimals).

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Expected Value
Variance
Cumulative Distribution Function

Formulas

P(X ≤ k) = F(k) for cumulative probability
P(X ≥ k) = 1 - F(k - 1)
E(X) = N * P
VAR(X) = N * P * (1 - P)

Theorems

Binomial Theorem
Properties of Binomial Distribution

Suitable Grade Level

College/University Level