The percentage of students passing exam is 20% (assume every student takes the test). You randomly select 32 graduating accounting students and would like to know a few things about their prospects of passing the test. Assume binomial distribution to answer the following questions.  Calculate the mean, variance, and standard deviation of the number of people passing the exam in this sample. What is the probability of exactly 12 students passing the test?   What is the probability of no more than 14 students passing the test?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The percentage of students passing exam is 20% (assume every student takes the test). You randomly select 32 graduating accounting students and would like to know a few things about their prospects of passing the test. Assume binomial distribution to answer the following questions. 

Calculate the mean, variance, and standard deviation of the number of people passing the exam in this sample.

What is the probability of exactly 12 students passing the test?  

What is the probability of no more than 14 students passing the test? 

What is the probability of at least 8 students passing the test? 

What is the probability of exactly 15 students failing the test? 

What is the 95th percentile of the distribution of the random variable: number of students passing the test? 

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