Question

The average incubation time for sea turtle eggs is approximately normally distributed with a mean of 57 days with a standard deviation of 7.3 days. Researches are trying to keep the beaches as safe as possible for the hatchlings to exit their nest and enter the sea. What is the probability that a randomly selected egg will hatch between 52 and 60 day

Answer 1

To find the probability that a randomly selected sea turtle egg will hatch between 52 and 60 days, we can use the normal distribution. The probability is approximately 0.5166, which means there is a 51.66% chance of hatching in this range.

Step-by-step explanation:

To find the probability that a randomly selected sea turtle egg will hatch between 52 and 60 days, we need to find the area under the normal distribution curve between these values.

First, we need to standardize the values using the z-score formula: z = (x - mean) / standard deviation.

So, the z-score for 52 days is z1 = (52 - 57) / 7.3 = -0.685 and the z-score for 60 days is z2 = (60 - 57) / 7.3 = 0.411.

Next, we use a standard normal distribution table or calculator to find the probability of the z-score falling between -0.685 and 0.411. The probability is approximately 0.5166, which means there is a 51.66% chance that a randomly selected egg will hatch between 52 and 60 days.