Test: Theoretical Distributions- 2 - CA Foundation MCQ

(Direction 4 - 27) Write down the correct answers. Each question carries 2 marks.

Q. What is the standard deviation of the number of recoveries among 48 patients when the probability of recovering is 0.75?

X is a binomial variable with n = 20. What is the mean of X if it is known that x is  symmetric?

If X ~ B (n, p), what would be the least value of the variance of x when n = 16?

If x is a binomial variate with parameter 15 and 1/3, what is the value of mode of the distribution

What is the no. of trials of a binomial distribution having mean and SD as 3 and 1.5 respectively?

What is the probability of getting 3 heads if 6 unbiased coins are tossed simultaneously?

If the overall percentage of success in an exam is 60, what is the probability that out of a group of 4 students, at least one has passed?

What is the probability of making 3 correct guesses in 5 True – False answer type questions?

If the standard deviation of a Poisson variate X is 2, what is P (1.5 < X < 2.9)?

If the mean of a Poisson variable X is 1, what is P (X = at least one)?

If X ~ P (m) and its coefficient of variation is 50, what is the probability that X would assume only non-zero values?

If 1.5 percent of items produced by a manufacturing units are known to be defective, what is the probability that a sample of 200 items would contain no defective item?

For a Poisson variate X, P (X = 1) = P (X = 2). What is the mean of X?

If 1 percent of an airline‘s flights suffer a minor equipment failure in an aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights?

If for a Poisson variable X, f(2) = 3 f(4), what is the variance of X?

What is the coefficient of variation of x, characterised by the following probability density

What is the first quartile of X having the following probability density function?

If the two quartiles of N (µ , σ²) are 14.6 and 25.4 respectively, what is the standard deviation of the distribution?

If the mean deviation of a normal variable is 16, what is its quartile deviation?

If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean deviation is

If the quartile deviation of a normal curve is 4.05, then its mean deviation  is

If the Ist quartile and mean deviation about median of a normal distribution are 13.25 and 8 respectively, then the mode of the distribution is

If the area of standard normal curve between z = 0 to z = 1 is 0.3413,  then the value of φ (1) is

If X and Y are 2 independent normal variables with mean as 10 and 12 and SD as 3 and 4, then (X+Y) is normally distributed with

(Direction 28 - 40) Answer the following questions. Each question carries 5 marks.

Q. If it is known that the probability of a missile hitting a target is 1/8, what is the probability that out of 10 missiles fired, at least 2 will hit the target?

X is a binomial variable such that 2 P(X = 2) = P(X = 3) and mean of X is known to be 10/3. What would be the probability that X assumes at most the value 2?

Assuming that one-third of the population are tea drinkers and each of 1000 enumerators takes a sample of 8 individuals to find out whether they are tea drinkers or not, how many enumerators are expected to report that five or more people are tea drinkers?