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Questions › IIT JAM › IIT JAM 2026 › Q42
1 markStatistics › Random variables and standard distributions › The normal distributionModerateabout 2 min

IIT JAM 2026 Question 42: Random variables and standard distributions

It is given that Prob(−1≤z≤1)=0.683\text{Prob}(-1\le z\le 1)=0.683Prob(−1≤z≤1)=0.683, Prob(−2≤z≤2)=0.954\text{Prob}(-2\le z\le 2)=0.954Prob(−2≤z≤2)=0.954, and Prob(−3≤z≤3)=0.997\text{Prob}(-3\le z\le 3)=0.997Prob(−3≤z≤3)=0.997, when zzz follows a standard normal distribution. If XXX follows a normal distribution with mean and variance as 5 and 4, respectively, then Prob(1≤X≤7)=\text{Prob}(1\le X\le 7)=Prob(1≤X≤7)= ________ (rounded off to three decimal places).

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Plain-text version

It is given that Prob(-1≤ z≤ 1)=0.683, Prob(-2≤ z≤ 2)=0.954, and Prob(-3≤ z≤ 3)=0.997, when z follows a standard normal distribution. If X follows a normal distribution with mean and variance as 5 and 4, respectively, then Prob(1≤ X≤ 7)= (*rounded off to three decimal places*).

Also written as: It is given that Prob(-1<= z<= 1)=0.683, Prob(-2<= z<= 2)=0.954, and Prob(-3<= z<= 3)=0.997, when z follows a standard normal distribution. If X follows a normal distribution with mean and variance as 5 and 4, respectively, then Prob(1<= X<= 7)= (*rounded off to three decimal places*).

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on The normal distribution, part of Random variables and standard distributions in Statistics.

The bell curve: standardising, tail probabilities and approximations.

TestStop has 20 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q31Let X ~ N(μ_X, σ_X²) and Y ~ N(μ_Y, σ_Y²). Which of the following is/are NOT correct?
  • IIT JAM 2021 · Q57Let X₁, X₂, X₃, X₄ be independent standard normal variables and Y = (X₁ + X₂)² + (X₃ + X₄)². The variance of…
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