Problem

For a standard normal distribution, find: \[ P(z<-0.95) \]

Solution

Step 1 :We are given a standard normal distribution and we need to find \(P(z<-0.95)\). This is the probability that a value from this distribution is less than -0.95.

Step 2 :To find this, we need to calculate the cumulative distribution function (CDF) at -0.95. The CDF of a standard normal distribution at a point x is given by the integral from negative infinity to x of the probability density function (PDF).

Step 3 :The PDF of a standard normal distribution is a complex function involving exponentials and square roots, but we can calculate the CDF directly.

Step 4 :By calculating, we find that \(P(z<-0.95)\) is approximately 0.171.

Step 5 :\(\boxed{\text{Final Answer: The probability that a value from a standard normal distribution is less than -0.95 is approximately 0.171.}}\)

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Source: https://solvelyapp.com/problems/16333/

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