SOLUTION: Research finds that of the students entering a degree program, 90% will successfully complete it. In 2018, 15 students commenced the course. Calculate the probability that: I) al

Question 1193467: Research finds that of the students entering a degree program, 90% will successfully complete it. In 2018, 15 students commenced the course. Calculate the probability that:
I) all 15 students will successfully complete the course.
II) only one student fails.
III) no more than two students fail.
I) at least two students fail.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Research finds that of the students entering a degree program, 90% will successfully complete it.
In 2018, 15 students commenced the course. Calculate the probability that:
I) all 15 students will successfully complete the course.
II) only one student fails.
III) no more than two students fail.
I) at least two students fail.
~~~~~~~~~~~~~~~~~

            All these problems/questions are about binomial probability distribution.
            So, use the related standard formulas.

(i)    P =  = 0.2059   (rounded).    ANSWER



(ii)   P =  =  = 0.34315   (rounded).     ANSWER



(iii)  "No more than two students fail" means 0, 1, or 2 students fail


       P = P(0 fail) + P(1 fails) + P(2 fail) = 

         =  +  +  = 

         =  = 0.8159    (rounded).    ANSWER



(iv)  "at least two students fail" means that no more than 1 student pass


       P = P(0 pass) + P(1 passes) =  +  =  = 1.36*10^(-13).     ANSWER

Solved.

RELATED QUESTIONS
Statistics collected over past years revealed that the percentage of students graduated... (answered by ewatrrr,ikleyn)

Research at the University of Toledo indicates that 50 percent of the students change... (answered by stanbon)

The pre-med adviser of a liberal arts college is trying to determine the proportion of... (answered by jrfrunner)

Research at Smallville University revealed that 50% of students change their major... (answered by stanbon)

4. Suppose that a school district wants to start a program for gifted students. The... (answered by Theo)

Hi..I try to solve this..but I got lost At Fictional University of Technology, 65% of (answered by stanbon)

1. high school dropouts. Approximately 10% of american high school students drop out of... (answered by stanbon)

An administrator at a Midwest university estimates that 12% of the female college... (answered by Theo)

To help students improve their reading, a school district decides to implement a reading... (answered by Boreal)