Suppose the lengths of human pregnancies are normally distributed with u = 266 days and o = 16 days. Complete parts (a) and (b) below. (a) The figure to the right represents the normal curve with u = 266 days and o = 16 days. The area to the right of X = 295 is 0.0350. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.)

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**Transcription of Educational Content on Human Pregnancy Duration Analysis**

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Suppose the lengths of human pregnancies are normally distributed with μ = 266 days and σ = 16 days. Complete parts (a) and (b) below.

(a) The figure to the right represents the normal curve with μ = 266 days and σ = 16 days. The area to the right of X = 295 is 0.0350. Provide two interpretations of this area.

Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.)

- ⃝ A. The proportion of human pregnancies that last more than [ ] days is [ ].
  
- ⃝ B. The proportion of human pregnancies that last less than [ ] days is [ ].

Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.)

- ⃝ A. The probability that a randomly selected human pregnancy lasts more than [ ] days is [ ].
  
- ⃝ B. The probability that a randomly selected human pregnancy lasts less than [ ] days is [ ].

**Graph Explanation:**
The graph is a standard bell-shaped normal distribution curve. The center of the curve is labeled as 266, which represents the mean (μ) pregnancy length in days. A vertical line is drawn at X = 295 on the distribution curve, indicating the point beyond which the area under the curve to the right is 0.0350. This area represents less than 5% of the distribution, implying that only a small proportion of pregnancies last longer than 295 days.

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This explanation helps in understanding normal distribution and probability interpretations related to the duration of human pregnancies.
Transcribed Image Text:**Transcription of Educational Content on Human Pregnancy Duration Analysis** --- Suppose the lengths of human pregnancies are normally distributed with μ = 266 days and σ = 16 days. Complete parts (a) and (b) below. (a) The figure to the right represents the normal curve with μ = 266 days and σ = 16 days. The area to the right of X = 295 is 0.0350. Provide two interpretations of this area. Provide one interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) - ⃝ A. The proportion of human pregnancies that last more than [ ] days is [ ]. - ⃝ B. The proportion of human pregnancies that last less than [ ] days is [ ]. Provide a second interpretation of the area using the given values. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals.) - ⃝ A. The probability that a randomly selected human pregnancy lasts more than [ ] days is [ ]. - ⃝ B. The probability that a randomly selected human pregnancy lasts less than [ ] days is [ ]. **Graph Explanation:** The graph is a standard bell-shaped normal distribution curve. The center of the curve is labeled as 266, which represents the mean (μ) pregnancy length in days. A vertical line is drawn at X = 295 on the distribution curve, indicating the point beyond which the area under the curve to the right is 0.0350. This area represents less than 5% of the distribution, implying that only a small proportion of pregnancies last longer than 295 days. --- This explanation helps in understanding normal distribution and probability interpretations related to the duration of human pregnancies.
### Text and Diagram Explanation for Educational Purposes

**Problem Statement:**

The figure to the right represents the normal curve with \( \mu = 266 \) days and \( \sigma = 16 \) days. The area between \( x = 230 \) and \( x = 250 \) is 0.1464. Provide two interpretations of this area.

**Interpretation Instructions:**

**First Interpretation:**

1. Select the correct choice below and fill in the answer boxes to complete your choice.
   - (Type integers or decimals. Use ascending order.)

   **Options:**
   - **A.** The proportion of human pregnancies that last between \(\_\_\_\) and \(\_\_\_\) days is \(\_\_\_\).
   - **B.** The proportion of human pregnancies that last less than \(\_\_\_\) or more than \(\_\_\_\) days is \(\_\_\_\).

**Second Interpretation:**

2. Provide another interpretation using the given values. Select the correct option below and fill in the answer boxes.
   - (Type integers or decimals. Use ascending order.)

   **Options:**
   - **A.** The probability that a randomly selected human pregnancy lasts less than \(\_\_\_\) or more than \(\_\_\_\) days is \(\_\_\_\).
   - **B.** The probability that a randomly selected human pregnancy lasts between \(\_\_\_\) and \(\_\_\_\) days is \(\_\_\_\).

**Graph Explanation:**

The graph represents a normal distribution curve with a mean (\( \mu \)) of 266 days and a standard deviation (\( \sigma \)) of 16 days. The shaded area between \( x = 230 \) and \( x = 250 \) represents the proportion of the total area under the curve, which is 0.1464. This area corresponds to a portion of pregnancies within that range of days.

The diagram visually illustrates how a normal distribution is concentrated around the mean, with areas under the curve indicating the probability or proportion of occurrences within specified intervals.
Transcribed Image Text:### Text and Diagram Explanation for Educational Purposes **Problem Statement:** The figure to the right represents the normal curve with \( \mu = 266 \) days and \( \sigma = 16 \) days. The area between \( x = 230 \) and \( x = 250 \) is 0.1464. Provide two interpretations of this area. **Interpretation Instructions:** **First Interpretation:** 1. Select the correct choice below and fill in the answer boxes to complete your choice. - (Type integers or decimals. Use ascending order.) **Options:** - **A.** The proportion of human pregnancies that last between \(\_\_\_\) and \(\_\_\_\) days is \(\_\_\_\). - **B.** The proportion of human pregnancies that last less than \(\_\_\_\) or more than \(\_\_\_\) days is \(\_\_\_\). **Second Interpretation:** 2. Provide another interpretation using the given values. Select the correct option below and fill in the answer boxes. - (Type integers or decimals. Use ascending order.) **Options:** - **A.** The probability that a randomly selected human pregnancy lasts less than \(\_\_\_\) or more than \(\_\_\_\) days is \(\_\_\_\). - **B.** The probability that a randomly selected human pregnancy lasts between \(\_\_\_\) and \(\_\_\_\) days is \(\_\_\_\). **Graph Explanation:** The graph represents a normal distribution curve with a mean (\( \mu \)) of 266 days and a standard deviation (\( \sigma \)) of 16 days. The shaded area between \( x = 230 \) and \( x = 250 \) represents the proportion of the total area under the curve, which is 0.1464. This area corresponds to a portion of pregnancies within that range of days. The diagram visually illustrates how a normal distribution is concentrated around the mean, with areas under the curve indicating the probability or proportion of occurrences within specified intervals.
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