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    Probability Distribution Exercises




    Hi guys,

    I got some big problems in Statistics and have actually no clue about 3 exercises I have to solve. If anyone can help me (even if its just one exercise) I would be so grateful. I will post them below:

    Question 1
    A student wants to apply for a job offered by an attractive and very wellknown
    company. The student expects to have very good exam results.
    The probability to be invited for an interview and to be employed by the
    firm is 5 per cent. This disencourages the student. Later the student hears
    that the probability of having very good exam results given that the
    company employs an applicant is 99 per cent. Furthermore he obtains the
    information that the probability of having very good exam results given
    that the company does not employ an applicant is 5 per cent. What is the
    probability for the student to be employed given that he has very good
    exam results?

    Question 2

    In a hotel it has been estimated that the average number of guests
    staying overnight is 100. It has also been found out that every day 20
    guests leave the hotel. If we randomly ask 10 guests in the morning how
    large is the probability that exactly 5 of them will leave the hotel?

    Question 3

    A tourist shop sells snacks including peanuts. When the stock of peanuts
    drops to 25 tins, a replenishment order is placed. It has been determined
    that the demand for peanuts during the replenishment lead-time is
    normally distributed with a mean of 20 tins and a standard deviation of 10
    tins. What is the probability that the demand during replenishment is
    greater than 25 tins?


    Thank you guys in advance.

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    Re: Probability Distribution Exercises

    Q1 is about conditional probability. You’ll need the following identities:
    P(A|B) × P(B) = P(B|A) × P(A) [Bayes’ theorem]
    P(¬X) = 1 – P(X)
    P(¬X|Y) = 1 – P(X|Y)
    With A = “Interviewed & employed” and B = “Very good exam results”, you can set up the knowns and unknowns and their relationships with those identities, and using a little algebraic manipulation you can solve for P(A|B) and P(B).

    Q2 is about a Poisson distribution with parameter λ = E(X) = 2 since we expect to have 2 guests leaving from 10 randomly selected ones.

    Q3 is about a normal distribution with μ = 20 and σ = 10. For x = 25, z = (25 – 20)/10 = 0.5 and the required probability P(x > 25) is the area under the N(0,1) curve for z > 0.5.

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    Re: Probability Distribution Exercises

    Thank you so much that helps a lot to solve the exercises.

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    Re: Probability Distribution Exercises


    Correction: Q2 is about a binomial distribution with p = 0.2 and n = 10. The Poisson distribution approximates it.

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