 # Find the specified areas for a standard normal density. 1.a.The area below z = 0.8. b.The area above = 1.2. c. The area between z = -1 and z = 2 tricotasu 2020-11-20 Answered
Find the specified areas for a standard normal density.
1.a.The area below z = 0.8.
b.The area above = 1.2.
c. The area between z = -1 and z = 2
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Step 1
The standard normal curve is the probability distribution curve of the normal random variable with mean 0 and standard deviation 1. The total area under the standard normal curve is 1.
Use standard normal table or z table to find the required probability.
(a) Observe the probability value in the z-table at 0.8 for z. The required area is 0.7881.
Hence,
$P\left(z<0.8\right)=0.7881$.
(b)
Observe the probability value in the z-table at 1.2 for z. The required area is 0.8849. Subtract the obtained probability value from 1 to obtain the area right to 1.2.
Hence,
$P\left(z>1.2\right)=1-0.8849=0.1151$
Step 2
(C)
$P\left(-1
$=0.9772-\left[1-P\left(z<1\right)\right]$
$=0.9772-\left[1-0.8414\right]$
=0.8185

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