Questions: The mean incubation time for a type of fertilized egg kept at a certain temperature is 23 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below. 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, exactly would be expected to hatch on day 21 or on day 23. B. In every group of 100 fertilized eggs, eggs would be expected to hatch between 21 and 23 days. C. If 100 fertilized eggs were randomly selected, 48 of them would be expected to hatch between 21 and 23 days. (e) Would it be unusual for an egg to hatch in less than 20 days? Why? The probability of an egg hatching in less than 20 days is 0.0013, so it would be unusual, since the probability is than 0.05. (Round to four decimal places as needed.)

The mean incubation time for a type of fertilized egg kept at a certain temperature is 23 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below. 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, exactly would be expected to hatch on day 21 or on day 23. B. In every group of 100 fertilized eggs, eggs would be expected to hatch between 21 and 23 days. C. If 100 fertilized eggs were randomly selected, 48 of them would be expected to hatch between 21 and 23 days. (e) Would it be unusual for an egg to hatch in less than 20 days? Why? The probability of an egg hatching in less than 20 days is 0.0013, so it would be unusual, since the probability is than 0.05. (Round to four decimal places as needed.)
Transcript text: The mean incubation time for a type of fertilized egg kept at a certain temperature is 23 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 1 day. Complete parts (a) through (e) below. 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, exactly $\square$ would be expected to hatch on day 21 or on day 23. B. In every group of 100 fertilized eggs, $\square$ eggs would be expected to hatch between 21 and 23 days. C. If 100 fertilized eggs were randomly selected, 48 of them would be expected to hatch between 21 and 23 days. (e) Would it be unusual for an egg to hatch in less than 20 days? Why? The probability of an egg hatching in less than 20 days is 0.0013 , so it $\square$ would be unusual, since the probability is $\square$ than 0.05 . (Round to four decimal places as needed.)
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Solution

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Solution Steps

Step 1: Probability of Hatching Between 21 and 23 Days

To find the probability of a fertilized egg hatching between 21 and 23 days, we calculated the probability using the normal distribution parameters:

  • Mean (\( \mu \)) = 23 days
  • Standard deviation (\( \sigma \)) = 1 day

The probability of hatching between 21 and 23 days is given by:

\[ P(21 < X < 23) = 0.4772 \]

Thus, the expected number of eggs hatching between 21 and 23 days out of 100 is:

\[ E = 100 \times P(21 < X < 23) = 100 \times 0.4772 = 48 \]

Step 2: Probability of Hatching in Less Than 20 Days

Next, we calculated the probability of a fertilized egg hatching in less than 20 days:

\[ P(X < 20) = 0.0013 \]

Step 3: Unusual Event Assessment

To determine if it is unusual for an egg to hatch in less than 20 days, we compare the probability to the threshold of 0.05:

Since \( P(X < 20) = 0.0013 < 0.05 \), it is indeed unusual for an egg to hatch in less than 20 days.

Final Answer

  • The expected number of eggs hatching between 21 and 23 days is \( \boxed{48} \).
  • It is unusual for an egg to hatch in less than 20 days, as the probability is \( \boxed{0.0013} \).
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