Questions: 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. (d) Find and interpret the probability that a randomly selected fertilized egg hatches between 11 and 15 days. The probability that a randomly selected fertilized egg hatches between 11 and 15 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. (Round to the nearest integer as needed.) A. If 100 fertilized eggs were randomly selected, of them would be expected to hatch between 11 and 15 days. B. If 100 fertilized eggs were randomly selected, exactly would be expected to hatch on day 11 or on day 15. C. In every group of 100 fertilized eggs, eggs would be expected to hatch between 11 and 15 days. (e) Would it be unusual for an egg to hatch in less than 9 days? Why? The probability of an egg hatching in less than 9 days is , so it be unusual, since the probability is

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. (d) Find and interpret the probability that a randomly selected fertilized egg hatches between 11 and 15 days. The probability that a randomly selected fertilized egg hatches between 11 and 15 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. (Round to the nearest integer as needed.) A. If 100 fertilized eggs were randomly selected, of them would be expected to hatch between 11 and 15 days. B. If 100 fertilized eggs were randomly selected, exactly would be expected to hatch on day 11 or on day 15. C. In every group of 100 fertilized eggs, eggs would be expected to hatch between 11 and 15 days. (e) Would it be unusual for an egg to hatch in less than 9 days? Why? The probability of an egg hatching in less than 9 days is , so it be unusual, since the probability is
Transcript text: 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. (d) Find and interpret the probability that a randomly selected fertilized egg hatches between 11 and 15 days. The probability that a randomly selected fertilized egg hatches between 11 and 15 days is $\square$ (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, $\square$ of them would be expected to hatch between 11 and 15 days. B. If 100 fertilized eggs were randomly selected, exactly $\square$ would be expected to hatch on day 11 or on day 15. C. In every group of 100 fertilized eggs, $\square$ eggs would be expected to hatch between 11 and 15 days. (e) Would it be unusual for an egg to hatch in less than 9 days? Why? The probability of an egg hatching in less than 9 days is $\square$ , so it $\square$ be unusual, since the probability is
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Solution

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Solution Steps

Step 1: Probability Calculation for Incubation Time Between 11 and 15 Days

To find the probability that a randomly selected fertilized egg hatches between 11 and 15 days, we calculate:

\[ P(11 < X < 15) = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(0.0) - \Phi(-2.0) = 0.4772 \]

Thus, the probability that a randomly selected fertilized egg hatches between 11 and 15 days is \( P = 0.4772 \).

Step 2: Interpretation of the Probability

If 100 fertilized eggs were randomly selected, the expected number of eggs that would hatch between 11 and 15 days is:

\[ \text{Expected eggs} = 100 \times P = 100 \times 0.4772 = 47.72 \approx 48 \]

Step 3: Probability Calculation for Incubation Time Less Than 9 Days

Next, we calculate the probability that an egg hatches in less than 9 days:

\[ P(X < 9) = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(-3.0) - \Phi(-\infty) = 0.0013 \]

Thus, the probability of an egg hatching in less than 9 days is \( P = 0.0013 \).

Step 4: Interpretation of the Probability for Hatching in Less Than 9 Days

Since the probability \( P = 0.0013 \) is significantly low, it would be unusual for an egg to hatch in less than 9 days.

Final Answer

The probability that a randomly selected fertilized egg hatches between 11 and 15 days is \( \boxed{0.4772} \). If 100 fertilized eggs were randomly selected, approximately \( \boxed{48} \) of them would be expected to hatch between 11 and 15 days. The probability of an egg hatching in less than 9 days is \( \boxed{0.0013} \), indicating that it would be unusual for an egg to hatch in less than 9 days.

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