Question

the mean incubation time for a type of fertilized egg kept at a certain temperature is 15 days. suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days. complete parts (a) through (e) below.
(a) draw a normal model that describes egg incubation times of these fertilized eggs.
choose the correct graph below.
click here to view graph a.
click here to view graph d.
click here to view graph c.
click here to view graph b.
(b) find and interpret the probability that a randomly selected fertilized egg hatches in less than 13 days.
the probability that a randomly selected fertilized egg hatches in less than 13 days is 0.1587.
(round to four decimal places as needed.)
interpret this probability. select the correct choice below and fill in the answer box to complete your choice.
(round to the nearest integer as needed.)
a. in every group of 100 fertilized eggs, 16 eggs would be expected to hatch in less than 13 days.
b. in every group of 100 fertilized eggs, 16 eggs would be expected to hatch in more than 17 days.
c. if 100 fertilized eggs were randomly selected, 16 of them would be expected to hatch on day 13.
(c) find and interpret the probability that a randomly selected fertilized egg takes over 17 days to hatch.
the probability that a randomly selected fertilized egg takes over 17 days to hatch is 0.1587.
(round to four decimal places as needed.)
interpret this probability. select the correct choice below and fill in the answer box to complete your choice.
(round to the nearest integer as needed.)
a. if 100 fertilized eggs were randomly selected, 16 of them would be expected to take more than 17 days to hatch.
b. in every group of 100 fertilized eggs, 16 eggs would be expected to hatch in more than 17 days.
c. if 100 fertilized eggs were randomly selected, 16 would be expected to hatch on day 17.

Explanation:

Step1: Interpret the probability for part (b)

The probability that a randomly selected fertilized egg hatches in less than 13 days is 0.1587. This means that if we were to randomly select many fertilized eggs, about 15.87% of them would hatch in less than 13 days.

Step2: Interpret the probability for part (c)

For part (c), we are looking at the probability that a randomly selected fertilized egg takes over 17 days to hatch. The probability is 0.1587. If we have a group of 100 fertilized eggs, we can use the formula \(n = p\times N\), where \(p = 0.1587\) and \(N=100\). So \(n=0.1587\times100 = 15.87\approx16\) (rounded to the nearest integer).

Answer:

• (b) If we randomly select many fertilized eggs, about 15.87% of them hatch in less than 13 days.
• (c) If 100 fertilized eggs were randomly selected, 16 of them would be expected to take more than 17 days to hatch.