To find the 16th percentile for incubation times, we need to use the properties of the normal distribution. The mean incubation time is given as 22 days, and the standard deviation is 1 day.
The 16th percentile is the value below which 16% of the data falls. In a standard normal distribution, we can find the z-score that corresponds to the 16th percentile by looking it up in the z-table or using a calculator that provides this function. The z-score for the 16th percentile is approximately -0.994.
Next, we use the z-score formula to convert the z-score back to the incubation time:
X = μ + (Z × σ)
Where:
X = value of the random variable
μ = mean (22 days)
Z = z-score (-0.994)
σ = standard deviation (1 day)
Substituting the values:
X = 22 + (-0.994 × 1)
X = 22 – 0.994
X ≈ 21.01
Therefore, the 16th percentile for incubation times is approximately 21.01 days.