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?
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%.
