Question

The mean incubation time for a type of fertilized egg kept at 100.2100.2â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 11 dayday. â(a) what is the probability that a randomly selected fertilized egg hatches in less than 2121 âdays? â(b) what is the probability that a randomly selected fertilized egg hatches between 2222 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?

Answer 1

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.