SOLUTION: 6.11 Suppose you are working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. Determine the value of x from the following informatio

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Question 1155714: 6.11 Suppose you are working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. Determine the value of x from the following information.
a. 60% of the values are greater than x.
b. x is less than 17% of the values.
c. 22% of the values are less than x.
d. x is greater than 55% of the values.
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
z=-0.253 for the 40th percentile. (60% are greater)
z=(x-mean)/sd
-.253=(x-200)/47
multiply through by 47
-11.89=x-200
x=188.11 -0.95
less than 17% of values.
z(.17)=-0.95
-.95=(x-200)/47
-44.8=x-200
155.2=x critical value
x<155.2 because want fewer than 17%
z(.22)=-0.77
-0.77+(x-200)/47
x-200=-36.3
x=163.7 critical value and answer.
.z(.55)=0.125
.125=(x-200)/47
5.90=x-200
x=205.90