GATE 2026 CE (CE2) – Question 47

Engineering Mathematics · Probability and Statistics: Random variables, Poisson and Normal distributions, linear regression · 2 marks · Numerical answer

The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed with a mean of 160 and standard deviation of 10.

If the probability of age greater than 50 years is equal to the probability of height greater than $h$, the value of $h$ (in cm) is ______ (*rounded off to two decimal places*).

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Correct answer: 170.81 to 172.53

Explanation

For age 50, $z = \frac{50 - 36}{12} = 1.1667$. Two normal variables have the same upper tail probability when they have the same $z$ value. So $\frac{h - 160}{10} = 1.1667$ and $h = 160 + 11.67 = 171.67$ cm.