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The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is
  • a)
    < 50%
  • b)
    50%
  • c)
    75%
  • d)
    100%
Correct answer is option 'A'. Can you explain this answer?
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To solve this problem, we need to use the standard normal distribution formula:

z = (x - μ) / σ

where z is the standard normal variable, x is the value we want to find the probability for (in this case, x = 1200), μ is the mean (μ = 1000), and σ is the standard deviation (σ = 200).

First, we need to calculate the z-score:

z = (1200 - 1000) / 200
z = 1

Next, we need to find the probability that the z-score is greater than 1. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the following command:

1 - normalcdf(-9999, 1)

This gives us a probability of approximately 0.1587.

Therefore, the probability that the annual precipitation will be more than 1200 mm is approximately 0.1587 or 15.87%.
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