All Free Statistics MCQs with Answers
Every Statistics question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.
545 questions · page 36 of 55
351. If Y=5X + 10 and X is N(10,25), then mean of Y is ?
- A. 135
- B. 50
- C. 70
- D. 60
Explanation: For a linear transformation, E(Y) = 5E(X) + 10. Substituting E(X) = 10 gives E(Y) = 5(10) + 10 = 60.
Correct answer: 60352. Area Under the normal curve on either side of mean is _____________?
- A. 1
- B. Mean value
- C. 0.5
- D. 2
- E. -1
Explanation: The normal curve is symmetric about its mean, so the total area is divided equally between the two sides. Each side has area 0.5, while the combined area on both sides is 1.
Correct answer: 0.5353. Which of the following parameter control the relative flatness of normal distribution?
- A. None
- B. Mode
- C. Standard Deviation
- D. Mean
Explanation: The standard deviation controls the spread of a normal curve: a larger value makes it wider and flatter, while a smaller value makes it narrower and taller. The mean only shifts the curve horizontally and does not alter its relative flatness.
Correct answer: Standard Deviation354. The shape of normal curve depends upon ?
- A. None
- B. Mean
- C. Quartile
- D. Standard Deviation
- E. Mean Deviation
Explanation: For a normal distribution, the standard deviation determines the curve's spread and therefore its shape or flatness. The mean changes the location of the curve, while quartiles and mean deviation do not serve as its defining parameters here.
Correct answer: Standard Deviation355. The value maximum ordinate of a standard normal curve at Z = 0 is:________?
- A. 1
- B. 0.5
- C. 0.3989
- D. None of these
Explanation: The standard normal density is highest at its centre, Z = 0, where its ordinate is 1 divided by √(2π), approximately 0.3989. This is a density height, not an area or probability.
Correct answer: 0.3989356. In normal distribution β1 = 0 and β2 is equal to _____________?
- A. 0.5
- B. 1
- C. 2
- D. 3
Explanation: A normal distribution has zero skewness, so β1 = 0. Its moment coefficient of kurtosis is β2 = 3, which is the mesokurtic benchmark.
Correct answer: 3357. For +ve and -ve skewed, check the sign of _______?
- A. β1
- B. µ2
- C. β2
- D. µ3
Explanation: The third central moment, μ3, carries the direction of skewness: it is positive for right skewness and negative for left skewness. β1 is based on a squared third moment and therefore cannot itself indicate the sign.
Correct answer: µ3358. Total area under the normal curve is________?
- A. 100
- B. 1
- C. 50%
- D. 1%
Explanation: The total probability represented by a continuous probability distribution is 1, so the entire area under the normal curve is 1, or 100%.
Correct answer: 1359. Normal distribution is _____ distribution?
- A. Symmetrical
- B. non-symmetrical
- C. + vely skewed
- D. -vely skewed
Explanation: The normal curve is symmetric about its mean, with equal left and right halves and zero skewness. Therefore it is neither positively nor negatively skewed.
Correct answer: Symmetrical360. Area to the right of (z=0) is the area for ____ values of z?
- A. Zero
- B. Negative
- C. Positive
- D. None of these
Explanation: Because z = 0 is the centre of the standard normal curve, values to its right are positive z-values. The area on that side is one-half, although the question is asking about the corresponding z values.
Correct answer: Positive