Question

The mean incubation time for a type of fertilized egg kept at 100.7100.7â°f is 2323 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 22 daysdays. 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 1919 and 2323 âdays? â(c) what is the probability that a randomly selected fertilized egg takes over 2525 days toâ hatch?

Answer 1

In this item, we have the mean incubation period of 23 days and the standard deviation is 22 days. We use z-score to determine the unknown in each of the items.

(a) less than 21 days.
       z-score = (23 - 21) / 22 = 1/11
This translates to a percentage of 53.6%

(b) z-score for 19 days.
     z-score = (23 - 19) / 22 = 2/11
This translates to a percentage of 57.2%.
   
    z-score for 23 days.
   z-score = (23 - 23)/ 22 = 0
This translates to a percentage of 50%.

The difference between the two numbers is only 7.2%

(c) z-score of 25.
     z-score = (23 - 25)/ 22 = -1/11
This translates to a percentage of 42.3%.

Then, subtract this value from 100 to give us the final answer of 57.2%.