Measures of dispersion — mean, median, mode of grouped and ungrouped data; standard deviation, variance and mean deviation for grouped and ungrouped data; probability — probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and binomial distribution.
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Q1 · Statistics and Probability · MEDIUM
The mean and variance of a binomial distribution are 4 and 3 respectively. What is the probability of getting exactly 2 successes?
Q2 · Statistics and Probability · EASY
A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
Q3 · Statistics and Probability · EASY
For a certain grouped data, the mean is 30 and the standard deviation is 5. If each observation is multiplied by 2 and then increased by 10, what will be the new standard deviation?
Q4 · Statistics and Probability · HARD
In a workshop, three machines A, B, and C produce 25%, 35%, and 40% of the total output respectively. The defective percentages for these machines are 5%, 4%, and 2% respectively. If a randomly selected item is found to be defective, what is the probability that it was produced by machine A?
Q5 · Statistics and Probability · MEDIUM
The median of the data 3, 5, 7, 9, x, x+2, 14, 16, 18, 20 is 11. Find the value of x.