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Punjab (PTB) · Chapter test · Free

1st Year Statistics Chapter 9 TestBinomial and Hyper Geometric Probability Distribution

30 marks · 40 minutes · 21 questions. Covers: CHAP 9: Binomial and Hyper Geometric Probability Distribution.

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1st Year Statistics Chapter 9 Test

1st Year · Statistics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. The number of trial in binomial distribution is:

    1. Not fixed

    2. Fixed

    3. Large

    4. Small

  2. The parameters of the hypergeometric distribution h(x; N, n, k) are:

    1. x, N, k

    2. N, n, k

    3. x, n, k

    4. x, N, n, k

  3. In which distribution the successive trials are without replacement?

    1. Hypergeometric distribution

    2. Binomial distribution

    3. Continuous distribution

    4. None of these

  4. For a given binomial distribution with n fixed, if p < 0.5, then

    1. The binomial distribution will be skewed to the left

    2. The binomial distribution will be skewed to the right

    3. The binomial distribution will be symmetric

    4. None of these

  5. The binomial distribution is negatively skewed if:

    1. p = 1

  6. Which of the following can never be described by a binomial distribution?

    1. The number of defective items produced by an assembly process

    2. The amount of water used by a single household

    3. The number of students in the class who can answer this question

    4. All of these can always be described by a binomial distribution

  7. The number of possible outcomes in a Bernoulli trial is:

    1. Three

    2. Four

    3. Two

    4. One

  8. In binomial distribution the range of X is:

    1. Zero to 

    2. Zero to n

    3. -1 to 

    4. Undefined

  9. In a binomial experiment, the successive trials are:

    1. Dependent

    2. Independent

    3. Mutually exclusive

    4. Fixed

  10. A fair die is rolled three times. The probability of getting three 'aces' is

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Find the probability i.e., tossing a fair coin four times there will appear 1 tail and 3 heads.

  2. Is it possible to have a binomial distribution in the following case: P(X = -2)=0.1467

  3. Define the binomial probability distribution.

  4. Define the Binominal Probability Distribution.

  5. Define binomial random variable.

  6. Find the mean and variance of the binomial distribution (q+p)3.

  7. Find the probability that in 5 tosses of a fair die '3 or 4' appears twice.

  8. Find the probability i.e., tossing a fair coin four times there will appear at the most 2 heads.

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. The experience of a house-agent that he can provide suitable accommodation for 75 percent of the clients who come to him. If one a particular occasion 6 clients approach him independently, calculate the probability that at least 5 clients will bet satisfactory accommodation.

  2. Suppose that the probability is 0.60 that a car stolen in a given city will be recovered. Find the probability that 3 out of 10 cars stolen in this city will be recovered.

  3. In a binomial distribution with n = 5, what is the value of other parameter of the binomial if P(X=0)=P(X=1)? Find its mean and variance.