I have in my possession a theoretical and practical test that evaluates the knowledge of a semester of the subject Probability and Statistics, that is, a written exam. The same is from July 30, 2013.
Clarification: I am not allowed to go online during an evaluation.
This test I am doing at home to evaluate myself.
Activity 1
The $ 35 $% of the students who took the first semester of the Computer Technologist, passed the subject MDyL1. It is considered a sample of $ 10 $ students of that semester and the random variable $ X $: number of students who have passed the subject MDyL1, among the selected $ 10 $.
- a) Calculate the probability that more than two students in the sample have passed the subject MDyL1.
- b) Find the probability that less than half of the students in the sample have passed the subject MDyL1.
- c) Determine $ E (X) $ and $ Var (X) $.
Can the random variable $X$ have a binomial distribution?
That is, each student pass a subject independently. It is known that the probability of that happening is $ p = 0.35 $, then the number of repetitions of that experiment should be $ n = 10 $.
That is, $ X $~$B (10,0.35)$, so that:
-Using the binomial distribution table-
a)
- $P(X>2) = 1-P(X≤2) = 1-0.2616 = 0.7384$
b)
- $P(X<5) = P(X≤4) = 0.7515$
c)
- $E(X) = np = 10 \times 0.35 = 3.5$
- $Var(X) = np(1-p) = 3.5 \times 0.65 = 2.275$
Is it okay to assume that each student passes a subject independently? Because the exercise does not clarify it. It says that 35% passes the subject, but not that each has a 35% chance of passing.
I hope you can help me. Thank you very much.