Suppose the birth weights of full-term babies are normally distributed with mean 3350 grams and standard deviation a = 485 grams. Complete parts (a) through (c) below. 3835 3350 4320 3350 2300 2s 3350 2380 4320 3350 2865 3835 4320 (c) Suppose the area under the normal curve to the right of X =320 is 0.0228. Provide an interpretation of this result. Select the correct choice below and fill in the answer box to complete your choice. (Type a whole number.) O A. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than grams. O B. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than grams.

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### Understanding Normal Distribution in Birth Weights

Suppose the birth weights of full-term babies are normally distributed with a mean (µ) of 3350 grams and a standard deviation (σ) of 485 grams. Below, we explore statistical analysis using this information.

#### Part (a) to (c) Analysis

We have the following normal distribution curves depicting different birth weights and their probabilities:

1. **Diagram Analysis**
   - **First Diagram:** The curve shows a shaded area to the right of \( x = 3835 \) grams.
   - **Second Diagram:** The curve displays a shaded area to the right of \( x = 3350 \) grams.
   - **Third Diagram:** The curve presents a shaded area to the right of \( x = 2865 \) grams.
   - **Fourth Diagram:** The curve indicates a shaded area to the right of \( x = 3835 \) grams and \( x = 4320 \) grams, depicting the tail ends of the distribution.

#### (c) Calculating Probabilities: Interpretation

Suppose the area under the normal curve to the right of \( X = 4320 \) is 0.0228. We need to provide an interpretation of this result:

- **Question for Interpretation:**
  Select the correct choice below and fill in the answer box to complete your choice. *(Type a whole number.)*

  - **Option A:** The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than \( \_\_\_\_\_\_ \) grams.
  - **Option B:** The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than \( \_\_\_\_\_\_ \) grams.

The answer to this interpretation will help in understanding the distribution of birth weights in full-term babies.

---

This educational material is designed to enhance your understanding of normal distribution and how it applies in real-life scenarios like birth weights. The diagrams visually represent different areas under the curve, which help in comprehending probability concepts associated with normal distribution.
Transcribed Image Text:--- ### Understanding Normal Distribution in Birth Weights Suppose the birth weights of full-term babies are normally distributed with a mean (µ) of 3350 grams and a standard deviation (σ) of 485 grams. Below, we explore statistical analysis using this information. #### Part (a) to (c) Analysis We have the following normal distribution curves depicting different birth weights and their probabilities: 1. **Diagram Analysis** - **First Diagram:** The curve shows a shaded area to the right of \( x = 3835 \) grams. - **Second Diagram:** The curve displays a shaded area to the right of \( x = 3350 \) grams. - **Third Diagram:** The curve presents a shaded area to the right of \( x = 2865 \) grams. - **Fourth Diagram:** The curve indicates a shaded area to the right of \( x = 3835 \) grams and \( x = 4320 \) grams, depicting the tail ends of the distribution. #### (c) Calculating Probabilities: Interpretation Suppose the area under the normal curve to the right of \( X = 4320 \) is 0.0228. We need to provide an interpretation of this result: - **Question for Interpretation:** Select the correct choice below and fill in the answer box to complete your choice. *(Type a whole number.)* - **Option A:** The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is less than \( \_\_\_\_\_\_ \) grams. - **Option B:** The probability is 0.0228 that the birth weight of a randomly chosen full-term baby in this population is more than \( \_\_\_\_\_\_ \) grams. The answer to this interpretation will help in understanding the distribution of birth weights in full-term babies. --- This educational material is designed to enhance your understanding of normal distribution and how it applies in real-life scenarios like birth weights. The diagrams visually represent different areas under the curve, which help in comprehending probability concepts associated with normal distribution.
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