SOLUTION: For Normal Distribution with mean &#956;=100 and standard deviation &#963;=20. find probability that x will be between x1 and x2: P (x1 < x < x2). Take x1 and x2 from the table

Algebra ->  Probability-and-statistics -> SOLUTION: For Normal Distribution with mean &#956;=100 and standard deviation &#963;=20. find probability that x will be between x1 and x2: P (x1 < x < x2). Take x1 and x2 from the table      Log On


   

Question 879541: For Normal Distribution with mean μ=100 and standard deviation σ=20.
find probability that x will be between x1 and x2: P (x1 < x < x2).
Take x1 and x2 from the table below.the value of x1 is 95 and the value of x2 is 110
********Here are steps to follow: convert x1 to z score z1, convert x2 to z score z2.
From Appendix table for Normal Distribution find area under curve
to the left of z1 and to the left of z2.
That will give you P (z < z1) and P (z < z2).
Then use formula: P (A < x < B) = P (z1 < z < z2) = P (z < z2) - P (z < z1)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Population: μ=100 and standard deviation σ=20.

 P (A < x < B) = P (z1 < z < z2) = P (z < z2) - P (z < z1)

 P (95 < x < 110) = 

P (-5/20 < z < 10/20) = P (x < .5) - P (z < .25) = .6815-.5987 = .0828

Below: find z-scores:  P (95 < x < 110) is the area under normal curve between z-values

For the normal distribution: Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  

Area under the standard normal curve to the left of the particular z is P(z)

Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50%  to the right