Babies born full-term (gestational period of 40 weeks) have a birth weight that follows a normal distribution, with mean 3300 gm and standard deviation 470 gm. (Include a labeled sketch. Round z-scores to 2 decimal places. Round probability to 4 decimal places.) What is the 10th percentile of birth weights of full-term babies? Round to one decimal place.
Babies born full-term (gestational period of 40 weeks) have a birth weight that follows a normal distribution, with mean 3300 gm and standard deviation 470 gm. (Include a labeled sketch. Round z-scores to 2 decimal places. Round probability to 4 decimal places.) What is the 10th percentile of birth weights of full-term babies? Round to one decimal place.
Babies born full-term (gestational period of 40 weeks) have a birth weight that follows a normal distribution, with mean 3300 gm and standard deviation 470 gm. (Include a labeled sketch. Round z-scores to 2 decimal places. Round probability to 4 decimal places.) What is the 10th percentile of birth weights of full-term babies? Round to one decimal place.
Babies born full-term (gestational period of 40 weeks) have a birth weight that follows a normal distribution, with mean 3300 gm and standard deviation 470 gm. (Include a labeled sketch. Round z-scores to 2 decimal places. Round probability to 4 decimal places.)
What is the 10th percentile of birth weights of full-term babies? Round to one decimal place.
Transcribed Image Text:The image depicts a standard normal distribution curve, commonly referred to as a "bell curve" due to its distinctive bell-shaped appearance. This curve is symmetrical, with its peak at the mean, median, and mode of the data set. The standard normal distribution is an essential concept in statistics, representing the distribution of many types of naturally occurring data.
### Key Characteristics of the Bell Curve:
1. **Symmetry**: The curve is perfectly symmetrical around the mean. This means that the left and right halves of the graph are mirror images of each other.
2. **Mean and Median**: The highest point on the curve is the mean (average) of the data set, which is also the median (the middle value) and the mode (the most frequently occurring value).
3. **Standard Deviation**: The spread of the curve is determined by the standard deviation. A smaller standard deviation results in a steeper and narrower bell curve, while a larger standard deviation results in a flatter and wider bell curve.
4. **Area Under the Curve**: The total area under the bell curve equals 1 (or 100%), representing the entire probability distribution of the dataset. The area under the curve within one standard deviation of the mean (on both sides) is approximately 68%, within two standard deviations is approximately 95%, and within three standard deviations is approximately 99.7%.
### Applications in Education:
Understanding the normal distribution is fundamental in various statistical analyses, including:
- **Standardized Testing**: Scores are often normalized to fit a bell curve, allowing educators to gauge student performance relative to peers.
- **Grading**: Some grading systems use the normal distribution to assign grades, ensuring a balanced distribution across different performance levels.
- **Research**: Many research studies assume normal distribution in their analysis, simplifying the process of drawing inferences and conclusions about the population studied.
In conclusion, the normal distribution curve is a crucial tool in educational settings and beyond, helping quantify and interpret data effectively.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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