The mean incubation time for a type of fertilized egg kept at a certain temperature is 24 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below. (Round to the nearest integer as needed) A. In every group of 100 fertilized eggs, eggs would be expected to hatch between 22 and 24 days (1) If 100 fertilized eggs were randomly selected exactly would be expected to hatch on day 22 or on day 24 If 100 fertilized eggs were randomly selected, 48 of them would be expected to hatch between 22 and 24 days (e) Would it be unusual for an egg to hatch in less than 21 days? Why? The probability of an egg hatching in less than 21 days is $\square$. so it be unusual. since the probability is than 0.05 (Round to four decimal places as neerded)
Solution
Step 1 ：The problem provides that the mean incubation time for a type of fertilized egg kept at a certain temperature is 24 days, and the incubation times are approximately normally distributed with a standard deviation of 1 day.
Step 2 ：For part A, we need to find the probability that an egg hatches between 22 and 24 days. This is equivalent to finding the cumulative distribution function (CDF) at 24 and subtracting the CDF at 22. The probability is approximately 0.4772.
Step 3 ：For part (1), we need to find the probability that an egg hatches on day 22 or 24. Since the incubation times are continuous, the probability of hatching on a specific day is technically zero. However, we can approximate this by finding the probability of hatching within a small interval around these days. The probability is approximately 0.4435.
Step 4 ：For part (e), we need to find the probability that an egg hatches in less than 21 days. This is equivalent to finding the CDF at 21. The probability is approximately 0.0013.
Step 5 ：Final Answer: In every group of 100 fertilized eggs, approximately \(\boxed{47.72\%}\) of eggs would be expected to hatch between 22 and 24 days. If 100 fertilized eggs were randomly selected, approximately \(\boxed{44.35\%}\) would be expected to hatch on day 22 or on day 24. The probability of an egg hatching in less than 21 days is \(\boxed{0.0013}\). So it would be unusual, since the probability is less than 0.05.
