Thank you for visiting The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 97 inches and a standard deviation of 10 inches. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The probability is 0.9192.
The question asks for the probability that the mean annual precipitation during 25 randomly picked years will be less than 99.8 inches. We are given that the annual precipitation amounts in the mountain range are normally distributed with a mean of 97 inches and a standard deviation of 10 inches.
To solve this problem, we can use the Central Limit Theorem. According to the theorem, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the sample size is large enough.
In this case, we are sampling 25 years, which is considered a large sample size. Therefore, we can assume that the sampling distribution of the mean will be approximately normally distributed.
To find the probability, we need to standardize the value of 99.8 inches using the formula z = (x - μ) / (σ / √n), where x is the value we want to standardize, μ is the mean, σ is the standard deviation, and n is the sample size.
Plugging in the values, we get z = (99.8 - 97) / (10 / √25) = 2.8 / 2 = 1.4.
Now, we can find the probability by looking up the z-score of 1.4 in the standard normal distribution table.
The probability that the mean annual precipitation during 25 randomly picked years will be less than 99.8 inches is approximately 0.9192, rounded to four decimal places.
In summary, the probability is 0.9192.
Learn more about probability from the given link
https://brainly.com/question/13604758
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