MATH 314 Homework 06

Due 2026-02-18 by 11:59pm

1. A software development team is working on improving the response time of an algorithm. Currently, when given random inputs, the algorithm successfully executes within the desired response time in 92% of cases. Suppose the team runs the algorithm with 100 random inputs as a testing phase.

   a. What is the probability that the algorithm will execute within the desired response time for exactly 95 out of the 100 inputs?

   b. What is the probability that the algorithm will execute within the desired response time for 90 or fewer of the 100 inputs?

   c. What is the probability that between 80 and 95 of the 100 inputs execute within the desired response time?

   d. On average, in how many cases do you expect the algorithm to successfully execute within the desired response time?