Question 1190763: . A random variable X has a normal distribution with mean 80 and standard deviation 4.8. What
is the probability that it will take a value:
A. Less than 87.2
B. Greater than 76.4
C. Between 81.2 and 86.0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can use the z-score table at https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf
first you want to find the z-score.
then you want to find the area to the left of the z-score.
than you want to find the area to the right of the z-score if that is what is being asked for.
for each of your problems you would do the following:
mean = 80
standard deviation = 4.8
. A random variable X has a normal distribution with mean 80 and standard deviation 4.8.
What is the probability that it will take a value:
A. Less than 87.2
z = (87.2 - 80) / 4.8 = 1.5
from the table, area to the left of that z-score = .93319.
that's the probability that you will get a score less than 87.2.
B. Greater than 76.4
z = (76.4 - 80) / 4.8 = -.75
from the table, area to the left of that z-score = .22663.
area to the right of that z-score = 1 minus .22663 = .77337.
that's the probability that you will get a score greater than 76.4.
C. Between 81.2 and 86.0
z1 = (81.2 - 80) / 4.8 = .25
area to the left of that z-score = .59871.
z2 = (86 - 80) / 4.8 = 1.25
area to the left of that z-score = .89435.
area in between = .89435 minus .59871 = .29564.
the table is arranged so that the z-score is in the left column.
that contains the z-score accurate to 1 decimal digit.
the next ten columns help you find the z-score accurate to 2 decimal digits.
column 2 adds .00 to the z-score in the left column.
column 3 adds .01 to the z-score in the left column.
column 4 adds .02 to the z-score in the left column.
this continue all the way to column 10.
column 10 adds .09 to the z-score in the left column.
an example is the area to the left of a z-score of 1.25.
you look down the left column to find a z-score of 1.2.
then you work to the right until you get to the column that has .05 heading.
the are shown there is the area to the left of a z-score of 1.25.
that would be equal to .89435.
you should be able to find the area to the left that i got abbove, using the table.
if you can't, let me know and i'll help you through it.
let me know if you have any questions.
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