SOLUTION: True or False? Support your answer. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 80

Algebra ->  Probability-and-statistics -> SOLUTION: True or False? Support your answer. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 80      Log On


   

Question 933739: True or False? Support your answer. If one score is randomly selected from a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score between X = 80 and X = 120 is p = 0.3413.
I would appreciate just a formula, I am not sure what to do to calculate the answer.
Thank you
JB
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
µ = 100 and σ = 20
.....
one score is randomly selected: z+=+blue%28x+-+100%29%2Fblue%2820%29
P( 80 < x <120) = P( -20/20 < z < 20/20) = normalcdf(-1,1) = .6826
0r
P( 80 < x <120) = P(z < 1) - P(z < -1) = .8413 - .1587 = .6826
.....
For the normal distribution: Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
68.26% of the Area under the standard normal curve is between z = -1 and z = 1
Note: 34.13% of the Area under the standard normal curve is between z = 0 and z = 1
...
Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50% to the right