## MCQs on Statistics

Solve Statistics Multiple-Choice Questions to prepare better for GATE. Learn more about Statistics and Statistics MCQs by checking notes, mock tests, and previous years’ question papers. Gauge the pattern of MCQs on Statistics by solving the ones that we have compiled below for your practice:

## Statistics Multiple-Choice Questions

**1.** Which of these is not true in terms of the probability distribution of any given continuous random variable?

a. Between two points a and b, the area present under the curve would represent the probability that X = a

b. Under the curve, the total area that is present will be equal to 1

c. We can find the range of the random variable on the X-axis

d. The probability density function is represented on the vertical coordinate

**Answer:** (a) Between two points a and b, the area present under the curve would represent the probability that X = a** **

**2.** Which of these does not refer to a normal distribution’s characteristics?

a. It is a type of bell-shaped distribution

b. The mean, mode and median are equal to each other

c. The mean will always be zero

d. It is a symmetrical type of distribution

**Answer:** (c) The mean will always be zero** **

**3.** Read the following statements and determine which of these is NOT true/correct?

a. The Poisson refers to a probability distribution for the discrete random variables while there is a continuous exponential distribution

b. The exponential distribution’s mean is equal to the inverse of Poisson’s mean

c. The exponential distribution refers to a family of various curves that are described totally by the mean

d. The Poisson process is described as some continuous random variable by the exponential distribution

**Answer:** (b) The exponential distribution’s mean is equal to the inverse of Poisson’s mean** **

**4.** For the exponential distribution that has a parameter Î», which of these statements would NOT stand true?

a. Since the standard deviation and mean are equal, this distribution would be a distribution of two parameters

b. The area that is present under the curve is equivalent to one

c. The standard deviation happens to be equal to 1/Î»

d. The mean would be equal to 1/Î»

**Answer:** (a) Since the standard deviation and mean are equal, this distribution would be a distribution of two parameters** **

**5.** The exponential density function and the normal distribution have which of these in common?

a. As x would approach infinity, both of these would approach zero

b. As x would approach infinity, both of these would approach infinity

c. Both of these are symmetrical types of distribution

d. Both of these are bell-shaped

**Answer:** (a) As x would approach infinity, both of these would approach zero** **

**6.** Which of these distributions is the best for measuring the total time elapsed between the arrival of vehicles at a gas station?

a. Binomial

b. Exponential

c. Normal

d. Uniform

e. Poisson

**Answer:** (b) Exponential** **

**7.** Assume that a test has 30 multiple choice questions, and every question has 4 different choices. Now assume that a student who hasn’t studied anything for this test decides to randomly answer all of these questions by guessing their answers. In this case, which of these probability distributions shall we use if we want to calculate the actual chance of this student getting a minimum of 20 right answers?

a. Poisson Distribution

b. Normal Distribution

c. Binomial Distribution

d. Exponential Distribution

**Answer:** (c) Binomial Distribution** **

**8.** Read the statements given below and identify which of these is NOT correctly applicable to the normal probability distributions?

a. Î¼ = 0 and Ïƒ = 1 for a standard normal distribution

b. The area that is covered under a probability curve is equivalent to one

c. These are unimodal (it means that these have single modes)

d. These have the very same standard deviation and mean

**Answer:** (d) These have the very same standard deviation and mean** **

**9.** Which of these cannot lead to a generation of Poisson distribution?

a. The total number of bacteria that lives in a cubic yard of soil

b. The total number of customers who are arriving at a petrol pump

c. The total number of phone calls that one can receive in an interval of ten minutes

d. The total number of misprints that one can find on a page

**Answer:** (b) The total number of customers who are arriving at a petrol pump** **

**10.** The mean of an exponential distribution happens to be equal to the mean of the Poisson distribution when the mean of the former distribution happens to be equal to:

a. 2.0

b. 0.25

c. 0.5

d. 1.0

**Answer:** (d) 1.0** **

**11.** The waiting time in front of an ATM machine in a very popular shopping mall is uniformly distributed between 1-5 minutes. What would be the probability of waiting between 2-4 minutes when someone wants to use this ATM?

a. 0.50

b. 0.25

c. 0.20

d. 0.75

**Answer:** (a) 0.50** **

**12.** Which of these statements would stand corrected for an f(x) probability density function?

a. With an increase in the value of X, the density function would also increase

b. For different values of the X, there will also be a difference in the height of the available density function

c. For all the values that we can assume for X, the density function would always remain constant

d. The density function would be “bell-shaped” roughly

e. None of the statements mentioned above is true

**Answer:** (c) For all the values that we can assume for X, the density function would always remain constant** **

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