Answer:
a) P [ Y ≤ -12 ] = 0,32997 or P [ Y ≤ -12 ] = 32,99 %
b) P [ Y > -1 ] = 0,3707 or P [ Y > -1 ] = 37,07 %
c) P [ 34 ≤ Y ≤ 44] = 0,1585 or P [ 34 ≤ Y ≤ 44] = 15,85 %
d) P [ Y > -4 ] = 0,59871 or P [ Y > -4 ] = 59,87 %
Step-by-step explanation:
Normal Distribution: N ( -8 ; 9 )
a) P [ Y ≤ -12 ] = ( - 12 - (-8))/9
P [ Y ≤ -12 ] = - 4/9 = - 0,44
From z-table for the z score -0,44 we get:
P [ Y ≤ -12 ] = 0,32997 or P [ Y ≤ -12 ] = 32,99 %
b) Normal Distribution: N ( - 4 ; 9 )
P [ Y > -1 ] = 1 - P [ Y ≤ -1 ]
P [ Y ≤ -1 ] = ( - 1 - ( - 4 ) ) / 9
P [ Y ≤ -1 ] = 3 / 9 = 0,3333
From z-table for the z score 0,33 we get:
P [ Y ≤ -1 ] = 0,6293
P [ Y > -1 ] = 1 - P [ Y ≤ -1 ] = 1 - 0,6293
P [ Y > -1 ] = 0,3707 or P [ Y > -1 ] = 37,07 %
c) Normal Distribution: N ( 40 ; 25 )
P [ 34 ≤ Y ≤ 44]
P [ 34 ≤ Y ≤ 44] = P [ Y ≤ 44] - P [ Y ≤ 34 ]
P [ Y ≤ 44] = ( 44 - 40 ) / 25 = 0,16
From z-table for the z score 0,16 we get:
P [ Y ≤ 44] = 0,5636
P [ Y ≤ 34 ] = ( 34 - 40 ) / 25 = - 6 / 25 = - 0,24
From z-table for the z score -0,24 we get:
P [ Y ≤ 34 ] = 0,40517
Then
P [ 34 ≤ Y ≤ 44] = P [ Y ≤ 44] - P [ Y ≤ 34 ]
P [ 34 ≤ Y ≤ 44] = 0,5636 - 0,40517
P [ 34 ≤ Y ≤ 44] = 0,1585 or P [ 34 ≤ Y ≤ 44] = 15,85 %
d) Normal Distribution: N ( -3 ; 4 )
P [ Y > -4 ] = 1 - P [ Y ≤ -4 ]
P [ Y ≤ -4 ] = ( - 4 - ( -3))/4 = - 1/4 = - 0,25
From z-table for the z score -0,25 we get:
P [ Y ≤ -4 ] = 0,40129
P [ Y > -4 ] = 1 - 0,40129
P [ Y > -4 ] = 0,59871 or P [ Y > -4 ] = 59,87 %
