# GATE Questions & Answers of Normal distribution

## What is the Weightage of Normal distribution in GATE Exam?

Total 6 Questions have been asked from Normal distribution topic of Probability and Statistics subject in previous GATE papers. Average marks 1.50.

The probability density function of evaporation E on any day during a year in a watershed is given by

The probability that E lies in between 2 and 4 mm/day in a day in the watershed is (in decimal) _____________

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If {x} is a continuous, real valued random variable defined over the interval (− ∞,+ ∞) and its occurrence is defined by the density function given as: $f\left(x\right)=\frac{1}{\sqrt{2\mathrm{\pi }}*b}{e}^{\frac{1}{2}{\left(\frac{x-a}{b}\right)}^{2}}$where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral ${\int }_{-\infty }^{a}\frac{1}{\sqrt{2\mathrm{\pi }}*b}{e}^{\frac{1}{2}{\left(\frac{x-a}{b}\right)}^{2}}dx$ is

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Find the value of λ such that the function f(x) is a valid probability density function. __________

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The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

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The standard normal probability function can be approximated as

$\mathrm{F}\left({x}_{\mathrm{N}}\right)=\frac{1}{1+\mathrm{exp}\left(-1.7255x{}_{\mathrm{N}}{\left|{x}_{\mathrm{N}}\right|}^{0.12}\right)}$

Where xN = standard normal deviate. If mean and standard deviation of annual precipitation are 102 cm and 27 cm respectively, the probability that the annual precipitation will be between 90 cm and 102 cm is

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If probability density function of a random variable X is

f(x) = x2 for -1 ≤ x ≤ 1, and
= 0 for any other value of x

Then, the percentage probability $P\left(-\frac{1}{3}\le x\le \frac{1}{3}\right)$ is