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 \( \boxed{0.0228} \).