For the standard normal distribution, find the following probabilities. (с) Pr(zleq 2.5)

York 2020-11-26 Answered
For the standard normal distribution, find the following probabilities.
(с) Pr(z2.5)
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Expert Answer

Asma Vang
Answered 2020-11-27 Author has 93 answers

The z score for a normally distribution of x is,
z=xμσ
Where, μ is the mean and σ 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(z25)=0.5+Pr(z<25)
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(0z2.5) is A2.5.
So the value of A2.5 from the appendix C is 0.4938.
The value of P(z2.5) is:
P(z<25)=05+0.4938=0.9938
Hence the value of P(z2.5) is 0.9938.

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