CA Foundation · Quantitative Aptitude · Theoretical Distributions
A continuous random variable X follows a normal distribution with mean 50 and standard deviation 10. If Z represents the standardised normal variate, what is the value of Z when X = 65?
The Z-score is calculated as (X - mean) divided by standard deviation. Here, Z = (65 - 50) / 10 = 1.5. This tells us that 65 is 1.5 standard deviations above the mean of the distribution.
- A0.5
- B1.5Correct
- C2.0
- D2.5
Explanation
Using the standardisation formula: Z = (X - μ) / σ = (65 - 50) / 10 = 15 / 10 = 1.5. This converts any normal distribution value to standard normal form where mean is 0 and standard deviation is 1.
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