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

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