Determine the following areas under the standard normal (z) curve: (round your answers to four decimal places.) (a) to the left of −1.29 (b) to the right of 1.29 (c) between −1 and 1 (d) to the left of 0 (e) to the right of −6 (f) between −1.7 and 2.5 (g) to the left of 0.23

a)   0.985

b)  0.0985

c) 0.6826

d)  0,5

e)  1

f) 0.9492

g)  0.5910

Step-by-step explanation:

a) Directly from z table: The area to the left of -1.29   is   0.985

b) To the right of 1.29  We get from z table the value of 0.9015 this value is the area from the point 1.29 up to the left tail, so we have to subtract            1 - 0.9015 and get  0.0985 (the area from the point 1.29 to the left)

c) Are between -1 and 1 . We find in z table values for 1  ( 0.8413 ) and for -1 ( 0.1587)  ( this last area is already included in the area of the point 1 so again we must subtract

0.8413 - 0.1587  = 0.6826

d) To the left of 0 the aea is 0,5

e) To the right of -6 is of course 1

f) Between -1.7 and 2.5 .  we find from z table the values

-1.7    ⇒   0.0446     (this area is included in the area of the point 2.5)           and for        2.5    ⇒ 0.9938

Then area between -1.7 and 2.5 is :  0.9492

g) Area to the left of 0.23 is directly fom z table : 0.5910

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,