Answer:
0.0823
Explanation:
we need to find z-score by using z-table and the formula, z = (x - υ) / υ where x is the observed value, υ is the mean and υ is the standard deviation.
z = (146.14 - 110) / 26
= 1.39.
now find the area relating to this z-score of 1.39 on a z-table.
go down the left column until to come to +1.3.
now find 0.09 on top row.
look where 1.3 and 0.09 meet.
the number is 0.9177.
that is the area to the left of z = 1.39. but we want area to right (question says probability it is greater).
total area under a bell curve (normal distribution) ALWAYS equals 1.
so area to right of z =1.39 is
1 - 0.9177
= 0.0823.
probability it is greater than 146.14 is 0.0823