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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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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.
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9c0c652-7fa5-4329-9b4d-671364bafb1a%2F94c3f58d-9f49-464c-a53f-df1596f21564%2Fxjdync_processed.jpeg&w=3840&q=75)
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