The annual precipitation data of a city with mean = 1000 mm and standard deviation = 200 mm. The probability that the annual precipitation will be more than 1200 mm is:Question 21Select one:a.>50%b.75%c.25 %d.<50 %
Question
The annual precipitation data of a city with mean = 1000 mm and standard deviation = 200 mm. The probability that the annual precipitation will be more than 1200 mm is:Question 21Select one:a.>50%b.75%c.25 %d.<50 %
Solution
To answer this question, we need to use the concept of standard deviation and the properties of a normal distribution.
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First, we need to calculate the z-score for the value of 1200 mm. The z-score is a measure of how many standard deviations an element is from the mean. The formula for the z-score is:
Z = (X - μ) / σ
where: X is the value we are interested in (1200 mm in this case), μ is the mean (1000 mm), σ is the standard deviation (200 mm).
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Plugging the values into the formula, we get:
Z = (1200 - 1000) / 200 = 1
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The z-score of 1 corresponds to a probability of about 0.8413 (or 84.13%) when we look it up in the z-table. This is the probability that the annual precipitation will be less than or equal to 1200 mm.
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However, we are interested in the probability that the annual precipitation will be more than 1200 mm. To find this, we subtract the probability we found from 1 (since the total probability must be 1):
P(X > 1200) = 1 - P(X ≤ 1200) = 1 - 0.8413 = 0.1587 (or 15.87%)
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Looking at the options, the closest one to our calculated probability is d. <50%.
So, the answer is d. <50%.
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