variable is normally distributed with mean 15 and standard deviation 3. a. Determine the quartiles of the variable. b. Obtain and interpret the 90th percentile. c. Find the value that​ 65% of all possible values of the variable exceed. d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025. Interpret the answer.

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A variable is normally distributed with mean 15 and standard deviation 3.
a. Determine the quartiles of the variable.
b. Obtain and interpret the 90th percentile.
c. Find the value that​ 65% of all possible values of the variable exceed.
d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025. Interpret the answer.
 
a. Q1=_____ Q2=_____ Q3=______
​(Round to two decimal places as​ needed.)
 
b. The 90th percentile is__________.
​(Round to two decimal places as​ needed.)
 
Choose the correct answer below.
A. The 90th percentile is the number that is 90​%
of the largest data value.
B. The 90th percentile is the number that occurs in the data 90​% of the time.
C. The 90th percentile is the number that divides the bottom 15​%
of the data from the top 90​% of the data.
D. The 90th percentile is the number that divides the bottom 90%
of the data from the top 15​% of the data.
 
c. The value that​ 65% of all possible values of the variable exceed is_______.
​(Round to two decimal places as​ needed.)
 
d. The two values that divide the area under the corresponding normal curve into a middle area of 0.95 and two outside areas of 0.025 are ______
and ______.
​(Round to two decimal places as needed. Use ascending​ order.)
 
These values enclose the area of the normal curve that is within_____
standard deviations.
​(Round to the nearest integer as​ needed.)
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