Question

For the standard normal distribution, find the following probabilities. (b) Pr(z>2.5)

Normal distributions
ANSWERED
asked 2021-01-08
For the standard normal distribution, find the following probabilities.
(b) \(Pr(z>2.5)\)

Expert Answers (1)

2021-01-09

The z score for a normally distribution of x is, \(z=\frac{x-\mu}{\sigma}\)
Where, \(\mu\) is the mean and \(\sigma\) is the standard deviation.
Calculation:
Consider the standard probability distribution, \(P (z > 2.5)\).
Now, the normal distribution is symmetric about mean 0.5.
So this implies,
\(P(z > 2.5) = 0.5 -Pr(z \leq 2.5)\)
The probability that the z lies between 0 and 2.5 is equal to the area that lies under the curve from 0 and 2.5.
To find the probability look in the column headed by z for the value of 2.5 in appendix C.
In the column headed by A across 2.5 the corresponding value is 0.4938.
Thus the probability \(P(0 \leq z \leq 2.5)\) is A_2.5.
So the value of \(A_{2.5}\) from the appendix C is 0.4938.
The value of \(P (z > 2.5)\) is:
\(P(z > 2.5) = 0.5 — 0.4938 = 0.0062\)
Hence the value of \(P(z > 2.5)\) is 0.0062.

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