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 %.

Question

Mathematics

Morrison

7 May, 12:14

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 %.

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Lauren Oliver · Answer 1

Answer: 22 days.

Step-by-step explanation:

The simplest approach in this problem is using the z scores. That's is computed by the fomular : z = (x - mean) / standard deviation ... (1).

In order to answer to the question. We need to find z-scores that have an area of 39% in the normal distribution plot. That means that there will be 61% on the outside of this range, and 39% within, centered around the mean.

Since we are interested in the two areas. We have 61%/2 = 30.5%. Now we have to find the z-score corresponding to a p-value of 0.305

From the normal table p-value of 0.305 corresponds with z = 0,6368. Now we need to Plug in the value we have for z, 21 for the mean and 1 for the standard deviation in equation (1) and solve for x.

We have 0,6368 = (x-21) / 1

Solving for x = 21 + 0,6368 = 21,6368 which approximately 22.