Math Problem Statement

The Alvin Secretarial Service procures temporary office personnel for major corporations. They have found that 50% of their invoices are paid within ten working days. A random sample of 18 invoices is checked. What is the probability that less than 15 of the invoices will be paid within ten working days? Round your answer to four decimal places.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

Binomial Probability Formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Binomial Cumulative Distribution Function (CDF): P(X < k) = sum of P(X = 0 to k-1)

Theorems

Binomial Theorem

Suitable Grade Level

Grades 10-12