SOLUTION: Can anyone help me with this? I need to show my work but not sure what steps I need to take to solve this. X has a normal distribution with a mean of 80.0 and a standard deviati

Click here to see ALL problems on Probability-and-statistics

Question 619302: Can anyone help me with this? I need to show my work but not sure what steps I need to take to solve this.
X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
(A) P(x < 77.0)
(B) P(75.0 < x < 85.0)
(C) P(x > 85.0)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:
----
The measuring stick you have to use to find probabilities
is the z-chart or technology that you have available.
-------------------------------
(A) P(x < 77.0)
z(77) = (77-80)/3.5 = -3/3.5 = -0.8571
That simply means 77 is 0.8571 standard deviations below the mean.
Now use your z-chart to find the probability to the left of -0.8571
Ans: normalcdf(-100,-0.8571) = 0.1957
--------------------------------------------
(B) P(75.0 < x < 85.0)
z(75) = (75-80)/3.5 = -1.4286
z(85) = (85-80)/3.5 = +1.4286
P(75 =================================
(C) P(x > 85.0)= P(z > 1.4286) = normalcdf(1.4286,100) = 0.0766
================
Cheers,
Stan H.
================