31. A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective?
32. A class of first year B. Tech. students is composed of four batches A, B, C and D, each consisting of 30 students. It is found that the sessional marks of students in Engineering Drawing in batch Chave a mean of 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are 5.5 and 4.2, respectively. It is
decided by the course instructor to normalize the marks of the students of all batches to have the same mean and standard deviation as that of the entire class. Due to this, the marks of a student in batch C are changed from 8.5 to
33. Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is
34. Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is
35. A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls?
36. It is estimated that average number of events during an year is three. What is the probability of occurrence of not more than two events over a two year duration? Assume that the number of events follow a Poisson's distribution.
37. Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3 ...., 20. What is the probability that 2 appears at an earlier position that any other even number in the selected permutation?
38. The standard normal cumulative probability function (probability from $$ - \infty $$ to xn) can be approximated as $${\text{F}}\left( {{{\text{x}}_{\text{n}}}} \right) = \frac{1}{{1 + {\text{exp}}\left( { - 1.7255{{\text{x}}_{\text{n}}}{{\left| {{{\text{x}}_{\text{n}}}} \right|}^{0.12}}} \right)}}$$ where xn = standard normal deviate. If mean and standard deviation of annual precipitation are 102 cm and 27 cm respectively, the probability that the annual precipitation will be between 90 cm and 102cm is
39. A probability distribution with right skew is shown in the figure.
The correct statement for the probability distribution is
The correct statement for the probability distribution is
40. Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown. If P(X ≤ -1) = P(Y ≥ 2) the standard deviation of Y is
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