NIMCET 2025 Paper

Section: Mathematics

Question : 46 of 120

Marks: +1, -0

The scores of students in a national-level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the cumulative distribution value of the standard normal variable at 0.5 is 0.691 , then the probability that a randomly selected student scored between 450 and 500 is:

0.391
0.191
0.591
0.091

Validate

Solution:

Convert 450 to a Z-score:

Z=\;{450-500}/{100}=-0.5

Given:

Φ(0.5)=0.691

Because the normal curve is symmetric:

Φ(-0.5)=1-Φ(0.5)=1-0.691=0.309

Probability between 450 and 500:

P(450< X< 500)=Φ(0)-Φ(-0.5)

=0.5-0.309=0.191

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