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Normal Distribution MCQs

Normal Distribution MCQs are multiple-choice questions on the bell-shaped continuous probability distribution, covering its parameters, z scores, quartiles, moments, kurtosis and areas under the curve. They help statistics students and lecturer test candidates revise a central topic. Every question comes with an instant answer, so you can check calculations and properties quickly.

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Question 18 Normal Distribution

P95 means?

Correct answer C. The point above below which 95% area lies

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About Normal Distribution MCQs

This Statistics topic tests both properties and quick calculations. Questions ask for the quartiles and quartile deviation in terms of mean and standard deviation, the z score of the mode, the fourth central moment, the parameter that controls the flatness of the curve, and probabilities such as P(6 ≤ X ≤ 10) for a given mean and standard deviation. Notation items like X ~ N(55, 49), skewness checks and percentile meanings such as P95 also appear.

The normal distribution underpins sampling, estimation and hypothesis testing, so it appears in nearly every statistics paper. Many questions can be solved in seconds once you know a few standard results and how to standardise a value. Practising these MCQs prepares you for statistics lecturer tests, PPSC and FPSC statistician posts, UGC NET and university exams, and strengthens the foundations needed for later inference topics.

Key facts to remember

  • In a normal distribution, the mean, median and mode are equal.
  • The standard normal variable Z = (X − μ)/σ has mean 0 and standard deviation 1.
  • About 68.27 percent of values lie within one standard deviation of the mean.
  • The quartile deviation of a normal distribution is about 0.6745σ, roughly two thirds of σ.
  • For a normal distribution the fourth central moment μ₄ equals 3σ⁴, giving kurtosis 3.
  • In N(μ, σ²) notation, the second value is the variance, not the standard deviation.

Exams that include Normal Distribution MCQs

Pakistan

  • PPSC
  • FPSC
  • SPSC
  • KPPSC
  • Lecturer tests

India

  • UGC NET
  • State PSC exams
  • Campus placements

Bangladesh

  • BCS
  • Government job tests

How to prepare for Normal Distribution MCQs

  1. Memorise the standard constants: quartiles at μ ± 0.6745σ, mean deviation about 0.7979σ and μ₄ = 3σ⁴.
  2. Always check whether N(μ, σ²) gives variance or standard deviation before standardising a value.
  3. Learn the areas for z = 1, 2 and 3 so you can estimate probabilities without full tables.
  4. Use symmetry: the area to the left of −z equals the area to the right of z.

Frequently asked questions

What are the main properties of the normal distribution?

It is continuous, symmetric and bell-shaped, with mean, median and mode equal at the centre. It is defined by its mean and standard deviation, the total area under the curve is 1, it has zero skewness and its kurtosis equals 3. The tails approach but never touch the horizontal axis.

How many Normal Distribution MCQs are on MCQs360?

There are 58 Normal Distribution MCQs on MCQs360 in the Statistics subject. Each question gives an instant answer, and the set is free to practise without signing up, making it handy before statistics papers. Many items need only a standard constant or a quick z score.

How do you find a probability using the normal distribution?

Convert each value to a z score with Z = (X − μ)/σ, then read the areas from a standard normal table. For example, with μ = 8 and σ = 4, P(6 ≤ X ≤ 10) becomes P(−0.5 ≤ Z ≤ 0.5), which is about 0.383.

Which exams ask Normal Distribution MCQs?

These questions appear in statistics lecturer tests and statistician posts set by PPSC, FPSC, SPSC and KPPSC in Pakistan, UGC NET and State PSC statistics papers in India, and BCS statistics cadre and related government tests in Bangladesh.

Last reviewed October 2026