SOLUTION: 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 fou

Question 129826: 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 μ = 6.8 hours and standard deviation σ = 2.1 hours.
Convert each of the following x intervals to standardized z intervals:
a) x ≤ 7.5
b) 5 ≤ x ≤ 8
c) x ≥ 4
Convert each of the following z intervals to raw score x intervals:
d) z ≥ -2
e) 0 ≤ z ≤ 2
f) z ≤ 3

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 μ = 6.8 hours and standard deviation σ = 2.1 hours.
----------------------
Comment:
Convert each of the following x intervals to standardized z intervals:
Comment: For each of these problems you have to find the z-value of the
given x-value. Then find the probility z satisfies the corresponding
inequality. I'll work the 1st one:
-------------
a) x ≤ 7.5
z(7.5) = (7.5-6.8)/2.1 = 0.3333333...
P(z<=7.7) = P(z<=0.333333333) = 0.6306
----------------------
b) 5 ≤ x ≤ 8
c) x ≥ 4
Convert each of the following z intervals to raw score x intervals:
Use the same transformation formula but solve for "x":
I'll work the 1st one.
----------
d) z ≥ -2
z = (x-mu)/sigma
So, x = z*sigma + mu
x = -2*2.1+6.8
x = 2.6
-------
P(z>=-2) = P(x >= 2.6)
-----------------------
e) 0 ≤ z ≤ 2
f) z ≤ 3
============================
Cheers,
Stan H.

RELATED QUESTIONS
let x be a random variable that represents the length of time it takes a student to write (answered by robertb)

Let x be a random variable that represents the length of time it takes a student to write (answered by stanbon)

Can somone please tell me how to do this i am so confused. Let X be a random variable... (answered by stanbon)

A small motor starts on the first attempt 3/8 of the time, on the second attempt 1/4 of... (answered by ikleyn)

Suppose a fair coin is tossed three times. Let X be the random variable that represents... (answered by yurtman,ikleyn)

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of... (answered by ewatrrr)

For Adam the probability a bull's eye with a bow and arrow is .4. Adam will take 5... (answered by stanbon,edjones)

5. Old-fashioned mechanical alarm clocks were not all that accurate. Suppose that the... (answered by ikleyn)

During a charity ride Sally and Ruth each cycle 120 km. Ruth�s average speed for the... (answered by josmiceli)