GATE CE 2026 Set 2 — Question 47
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Engineering Mathematics → Probability → Normal Distribution
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Question
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 , the value of (in cm) is ______ (rounded off to two decimal places).
Correct answer
170 to 173
Solution
Let be the age and be the height.
We are given that .Step 1: Convert the age condition to the standard normal variable .So, .Step 2: Convert the height condition to the standard normal variable .So, .Step 3: Equate the -scores since the probabilities are equal.Rounding to two decimal places, we get 171.67.
We are given that .Step 1: Convert the age condition to the standard normal variable .So, .Step 2: Convert the height condition to the standard normal variable .So, .Step 3: Equate the -scores since the probabilities are equal.Rounding to two decimal places, we get 171.67.
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