Problem

Find the area under the standard normal curve to the right of $z=-2.37$. Round your answer to four decimal places,

Solution

Step 1 :We are given a standard normal curve and we are asked to find the area to the right of $z=-2.37$. The area under the standard normal curve to the right of any point is given by the cumulative distribution function (CDF) of the standard normal distribution at that point. The CDF at any point $z$ is given by $P(Z \leq z)$, where $Z$ is a standard normal random variable. However, we want $P(Z > -2.37)$, which is equal to $1 - P(Z \leq -2.37)$.

Step 2 :We can calculate this using the scipy library in Python. The code would be: ```python from scipy.stats import norm z = -2.37 area = 1 - norm.cdf(z) print(area) ``` When we run this code, we get the area as approximately 0.9911059573696632.

Step 3 :Rounding this to four decimal places, we get 0.9911.

Step 4 :Final Answer: The area under the standard normal curve to the right of $z=-2.37$ is approximately \(\boxed{0.9911}\).

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Source: https://solvelyapp.com/problems/oZQQFtB2b0/

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