SOLUTION: Can somone please tell me how to do this i am so confused. Let X be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's

Question 153427: Can somone please tell me how to do this i am so confused.
Let X be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that X has an approximately normal distribution with mean U = 6.8 hours and standard deviation O=2.1 hours.
Convert each of the following X intervals to standardized Z intervals:
a) x is less than or equal to 7.5
b) 5 is less than or equal to X is less than or equa to 8
c) x is greater than or equal to 4
Convert each of the following z intervals to raw score X intervals
d) z is greater than or equal to -2
e) 0 is less than or equal to Z is less than or equal to 2
f) Z is less than or equal to 3
Thank you for your help in advance
jill
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
After interviewing many students, it was found that X has an approximately normal distribution with mean U = 6.8 hours and standard deviation O=2.1 hours.
Convert each of the following X intervals to standardized Z intervals:
a) x is less than or equal to 7.5
Find the z score of 7.5
z(7.5) = (7.5-6.8)/2.1 = 0.333333...
z-interval: z <= 0.33333....
------------------------------------------
b) 5 is less than or equal to X is less than or equal to 8
z(5) = (5-6.8)/2.1 = -0.8571...
z(8) = (8-6.8)/2.1 = 0.5714...
z-interval: (-0.8571 < z < 0.5714)
-----------------------------------------------
c) x is greater than or equal to 4
Find z(4) then write the z-interval.
------------------------------------------
Convert each of the following z intervals to raw score X intervals
d) z is greater than or equal to -2
x(z) = sigma*z + u
x(-2) = 2.1*-2 + 6.8 = 2.6
x-interval: x >= 2.6
--------------------------------
e) 0 is less than or equal to Z is less than or equal to 2
x(0) = 2.1*0 + 6.8 = 6.8
x(2) = 2.1*2 + 6.8 = 11
x-interval : 6.8 <= x <= 11
--------------------------------
f) Z is less than or equal to 3
Use the same process on this problem.
=============================
Cheers,
Stan H.

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