Probability Distributions Two Marks Question

12th Standard EM

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. In a family of 3 children, what is the probability that there will be exactly 2 girls?

  2. Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects.

  3. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes.

  4. The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

  5. Write any 2 examples for Poisson distribution.

  6. Write the conditions for which the poisson distribution is a limiting case of binomial distribution.

  7. Derive the mean and variance of poisson distribution.

  8. The average number of phone calls per minute into the switch board of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be
    (i) no phone at all
    (ii) exactly 3 calls
    (iii) atleast 5 calls

  9. Define Standard normal variate.

  10. In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution.

  11. X is normally distributed with mean 12 and sd 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)

  12. A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain
    (a) no more than 2 rejects?
    (b) at least 2 rejects?

  13. The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time .
    a) less than 19.5 hours?
    b) between 20 and 22 hours?

  14. X is a normally normally distributed variable with mean μ = 30 and standard deviation σ = 4. Find
    (a) P(x < 40)
    (b) P(x > 21)
    (c) P(30 < x < 35)

  15. People’s monthly electric bills in chennai are normally distributed with a mean of Rs.225 and a standard deviation of Rs. 55. Those people spend a lot of time online. In a group of 500 customers, how many would we expect to have a bill that is Rs. 100 or less?

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