To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.
The formula for z score is:
z = (x – u) / s
where,
x = sample value
u = sample mean = 23 days
s = standard deviation = 1 day
A. P when x < 21 days
z = (21 – 23) / 1
z = -2
Using the table,
P = 0.0228
Therefore there is a 2.28% probability that the hatching period is less than 21 days.
B. P when 23 ≥ x ≥ 22
z (x=22) = (22 – 23) / 1 = -1
P (z=-1) = 0.1587
z (x=23) = (23 – 23) / 1 = 0
P (z=0) = 0.5
P = 0.5 - 0.1587 = 0.3413
Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.
C. P when x > 25
z = (25 – 23) / 1
z = 2
P = 0.9772
This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:
P true = 1 – 0.9772
P true = 0.0228
Therefore there is a 2.28% probability that the hatching period is more than 25 days.