Question

4. The mean incubation time for a type of fertilized egg kept at a certain temperature is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Draw a normal model that describes egg incubation times of these fertilized eggs. Choose the correct graph below. O O O O Click here to view graph b. Click here to view graph a. Click here to view graph d. Click here to view graph c. (b) Find and interpret the probability that a randomly selected fertilized egg hatches in less than 20 days. The probability that a randomly selected fertilized egg hatches in less than 20 days is (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. O A. The average proportion of the way to hatching of all eggs fertilized in the past 20 days is (Round to two decimal places as needed.) eggs will hatch in less than 20 days. OB. In every group of 100 fertilized eggs. (Round to the nearest integer as needed.) O c. If 100 fertilized eggs were randomly selected, (Round to the nearest integer as needed.) of them would be expected to hatch in less than 20 days. (c) Find and interpret the probability that a randomly selected fertilized egg takes over 24 days to hatch. The probability that a randomly selected fertilized egg takes over 24 days to hatch is (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. O A. In every group of 100 fertilized eggs, eggs will hatch in more than 24 days. (Round to the nearest integer as needed.) OB. The average proportion of the way to hatching of all eggs fertilized more than 24 days ago is (Round to two decimal places as needed.) O c. If 100 fertilized eggs were randomly selected, of them would be expected to take more than 24 days to hatch. (Round to the nearest integer as needed.) (d) Find and interpret the probability that a randomly selected fertilized egg hatches between 21 and 22 days. The probability that a randomly selected fertilized egg hatches between 21 and 22 days is (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. O O A. If 100 fertilized eggs were randomly selected, of them would be expected to hatch between 21 and 22 days. (Round to the nearest integer as needed.) B. In every group of 100 fertilized eggs, eggs will hatch between 21 and 22 days. (Round to the nearest integer as needed.) O C. The average proportion of the way to hatching of all eggs fertilized between 21 and 22 days is (Round to two decimal places as needed.) (e) Would it be unusual for an egg to hatch in less than 19 days? Why? so it (1) be unusual, since the probability is (2) — than The probability of an egg hatching in less than 19 days is 0.05. (Round to four decimal places as needed.)

Answer 1

a) Option - D graph or the last graph is the correct graph.

b) P(X < 20)

= P((X - )/ < (20 - )/)

= P(Z < (20 - 22)/1)

= P(Z < -2)

= 0.0228

Option - C) If 100 fertilized eggs were randomly selected , 2 of them would be expected to hatch in less than 20 days.

c) P(X > 24)

= P((X - )/ > (24 - )/)

= P(Z > (24 - 22)/1)

= P(Z > 2)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

Option - C) If 100 fertilized eggs were randomly selected , 2 of them would be expected to take more than 24 days to hatch.

d) P(21 < X < 22)

= P((21 - )/ < (X - )/ < (22 - )/)

= P((21 - 22)/1 < Z < (22 - 22)/1)

= P(-1 < Z < 0)

= P(Z < 0) - P(Z < -1)

= 0.5 - 0.1587

= 0.3413

Option - A) If 100 fertilized eggs were randomly selected , 34 of them would be expected to hatch between 21 and 22 days.

e) P(X < 19)

= P((X - )/ < (19 - )/)

= P(Z < (19 - 22)/1)

= P(Z < -3)

= 0.0013The probability of an egg hatching less than 19 days is 0.0013, so it would be unusual, Since the probability is less than 0.05.