TERM3 6. Kaseyann Anderson 11/19/23 10:19 AM 2 Question 14, 7.2.RA-3 HW Score: $1.67 \%, 0.25$ of 15 points Points: 0 of 1 Sav The mean incubation time of fertilized eggs is 22 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. Determine the incubation times that make up the middle $39 \%$. Click the icon to view a table of areas under the normal curve. The incubation times that make up the middle $39 \%$ are $\square$ to $\square$ days (Round to the nearest whole number as needed. Use ascending order.) Clear all Check answer

Step 1 ：The problem is asking for the incubation times that make up the middle 39% of a normal distribution with a mean of 22 days and a standard deviation of 1 day.

Step 2 ：We can use the properties of the normal distribution to solve this problem. The middle 39% of the distribution corresponds to the cumulative probabilities of 0.305 and 0.695.

Step 3 ：We can find the z-scores corresponding to these cumulative probabilities using the inverse of the cumulative distribution function (CDF) for a standard normal distribution. The z-score is the number of standard deviations away from the mean a particular value is.

Step 4 ：The z-scores corresponding to the cumulative probabilities of 0.305 and 0.695 are approximately -0.51 and 0.51, respectively.

Step 5 ：We can then use the formula for the z-score, \(Z = (X - \mu) / \sigma\), to find the corresponding incubation times. Here, \(\mu\) is the mean and \(\sigma\) is the standard deviation. We can rearrange the formula to solve for X: \(X = Z*\sigma + \mu\).

Step 6 ：Substituting the values into the formula, we get the incubation times as approximately 21 and 23 days.

Step 7 ：Rounding these values to the nearest whole number as needed, we get the final answer.

Step 8 ：The incubation times that make up the middle 39% of the distribution are 21 to 23 days. This means that 39% of the incubation times lie between 21 and 23 days.

Step 9 ：Final Answer: The incubation times that make up the middle $39 \%$ are \(\boxed{21}\) to \(\boxed{23}\) days.