The mean incubation time for a type of fertilized egg kept at a certain temperature is 19 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below.

Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
Click here to view graph a.
(b) Find and interpret the probability that a randomly selected fertilized egg hatches in less than 17 days

The probability that a randomly selected fertilized egg hatches in less than 17 days is $\square$.
(Round to four decimal places as needed.)

Step 1 ：Given that the mean incubation time for a type of fertilized egg kept at a certain temperature is 19 days and the standard deviation is 1 day, we are asked to find the probability that a randomly selected fertilized egg hatches in less than 17 days.

Step 2 ：To solve this problem, we first convert the incubation time of 17 days to a z-score. The z-score is a measure of how many standard deviations an element is from the mean. The formula for calculating the z-score is \( (X - \mu) / \sigma \), where X is the value we are interested in, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.

Step 3 ：Substituting the given values into the formula, we get \( z = (17 - 19) / 1 = -2.0 \).

Step 4 ：We then use a standard normal distribution table to find the probability corresponding to this z-score. The probability that a randomly selected fertilized egg hatches in less than 17 days is approximately 0.0228.

Step 5 ：This means that there is about a 2.28% chance that a randomly selected fertilized egg will hatch in less than 17 days.

Step 6 ：So, the final answer is: The probability that a randomly selected fertilized egg hatches in less than 17 days is \( \boxed{0.0228} \).