the annual precipitation amounts in a certain mountain range are normally distributed with a mean of 85 inches, and a standard deviation of 13 inches. what is the probability that the mean annual precipitation during 49 randomly picked years will be less than 87.6 inches?

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20-12-2022
Mathematics

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the annual precipitation amounts in a certain mountain range are normally distributed with a mean of 85 inches, and a standard deviation of 13 inches. what is the probability that the mean annual precipitation during 49 randomly picked years will be less than 87.6 inches?

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kumarravichandra kumarravichandra · Answer 1 · 2022-12-22T22:22:36-05:00

The probability that the mean annual precipitation during 49 randomly picked years will be less than 87.6 inches is 0.84. This can be calculated using the Z-score formula:

(87.6 - 85) / (13 / √49) = 0.84.

The probability that the mean annual precipitation during 49 randomly picked years will be less than 87.6 inches can be calculated using the Z-score formula. This formula uses the mean, standard deviation, and number of samples to calculate a Z-score, which is then used to calculate the probability. In this case, the mean is 85 inches, the standard deviation is 13 inches, and the number of randomly selected years is 49. By plugging these values into the formula, we can calculate the Z-score, which is 0.84. This Z-score can then be used to calculate the probability, which is 0.84. This means that there is an 84% probability that the mean annual precipitation during 49 randomly picked years will be less than 87.6 inches.

(87.6 - 85) / (13 / √49) = 0.84

Learn more about z score here

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