Question

1. You have a X = 300, mean = 395, and a standard deviation = 39
   1. Find the area between the mean and the z-score. Show all your work

2. You have a X = 45, mean = 38, and a standard deviation = 4
   1. Find the area between the mean and the z-score. Show all your work

3. Find the area under the curve between the answers to question 1 and 2.

Answer 1

You have a X = 300, mean = 395, and a standard deviation = 39

we need to find the are between X = 300 and mean = 395

P[ 300 < X < 395 ] = P[ ( 300 - mean )/standard deviation < (X - mean )/standard deviation < ( 395 - mean )/standard deviation ]

P[ 300 < X < 395 ] = P[ ( 300 - 395 )/39 < ( X - 395 )/39 < ( 395 - 395 )/39 ]

P[ 300 < X < 395 ] = P[ -95/39 < Z < 0 ]

P[ 300 < X < 395 ] = P[ -2.4359 < Z < 0 ]

P[ 300 < X < 395 ] = P[ Z < 0 ] - P[ Z < -2.4359 ]

P[ 300 < X < 395 ] = 0.5 - 0.0074

P[ 300 < X < 395 ] = 0.4926

X = 45, mean = 38, and a standard deviation = 4

we need to find the are between X = 45 and mean = 38

P[ 38 < X < 45 ] = P[ ( 38 - mean )/standard deviation < (X - mean )/standard deviation < ( 45 - mean )/standard deviation ]

P[ 38 < X < 45 ] = P[ ( 38 - 38 )/4 < ( X - 38 )/4 < ( 45 - 38 )/4 ]

P[ 38 < X < 45 ] = P[ 0 < Z < 7/4 ]

P[ 38 < X < 45 ] = P[ 0 < Z < 1.75 ]

P[ 38 < X < 45 ] = P[ Z < 1.75 ] - P[ Z < 0 ]

P[ 38 < X < 45 ] = 0.9599 - 0.5

P[ 38 < X < 45 ] = 0.4599