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# Calculating the desired probability values

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Z is the standard normal random variable that is, the normal random variable with mean 0 and standard deviation 1. Use the table values in your textbook to determine the following

a. The probability that z is less than -2.12.

b. The probability that z is greater than 1.57.

c. The probability that z is between -1.84 and 0.60.

d. The value of z such that the area to the left of z is 0.4721.

e. The value of z such that the area to the right of z is 0.9958.

https://brainmass.com/statistics/probability/calculating-desired-probability-values-447662

## SOLUTION This solution is FREE courtesy of BrainMass!

a. The probability that z is less than -2.12.
Table gives the value of area under the curve between mean and Z value. So,
P(Z<-2.12)=0.50-P(-2.12<Z<0)=0.50-0.4830=0.017

b. The probability that z is greater than 1.57.
Table gives the value of area under the curve between mean and Z value. So,
P(Z>1.57)=0.50-P(0<Z<1.57)=0.50-0.4292=0.0708

c. The probability that z is between -1.84 and 0.60.
P(-1.84<Z<0.60)=P(-1.84<Z<0)+P(0<Z<0.60)=0.4671+.2257=0.6928

d. The value of z such that the area to the left of z is 0.4721.
Area to the left of Z is less than 0.50. It means that Z will have negative value.
P(Z<Zo)=0.4721
i.e. P(-Zo<Z<0)=0.50-0.4721=0.0279
Now look into the table for the area under the curve=0.0279, we find that for Z=0.07, area under the curve is 0.0279.
P(-0.07<Z<0)= 0.0279
So, Zo=-0.07

e. The value of z such that the area to the right of z is 0.9958.

Area to the right of z is more than 0.5, it means that z will have a negative value.
P(Z>Zo)=0.9958
P(Z>Zo)=P(-Zo<Z<0)+P(Z>0)
0.9958=P(-Zo<Z<0)+0.50
P(-Zo<Z<0)=0.9958-0.50
=0.4958

Now look into the table for the area under the curve=0.4958, we find that for Z=0.07, area under the curve is 0.4958.
We find that above value lies between 2.63 and 2.64.
P(-2.635<Z<0)= 0.4958
So, Zo=-2.635

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!