The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Choose the correct histogram below. Weight (g) 6.000-6.049 6.050-6.099 6.100-6.149 Frequency OA. Q 20 15 10- 3 7 6.150-6.199 10 6.200-6.249 11 6 6.1 6.2 6.3 6.250-6.299 Weight (grams) 6.300-6.349 OB. 6.350-6.399 15 10- Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not? 5- 6.1 62 6.3 Weight (grams) Oc. 15 6.1 62 6.3 Weight (grama)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters.
| Weight (g) | Frequency |
|--------------|-----------|
| 6.000-6.049 | 3 |
| 6.050-6.099 | 3 |
| 6.100-6.149 | 7 |
| 6.150-6.199 | 10 |
| 6.200-6.249 | 11 |
| 6.250-6.299 | 4 |
| 6.300-6.349 | 5 |
| 6.350-6.399 | 1 |
Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
### Choose the correct histogram below:
- **Option A**: Shows a bell-shaped distribution with frequencies that generally increase to a peak and then decrease, appearing roughly symmetric.
- **Option B**: Indicates frequencies initially decreasing then increasing, and the histogram appears roughly symmetric without a bell shape.
- **Option C**: Demonstrates frequencies that decrease to a minimum and then increase, forming a roughly symmetric distribution.
### Does the histogram appear to depict data that have a normal distribution?
- **Option A**: The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric.
- **Option B**: The histogram does not appear to depict a normal distribution. The frequencies decrease to a minimum and then increase, and the histogram is roughly symmetric.
- **Option C**: The histogram appears to depict a normal distribution. The frequencies generally decrease to a minimum and then increase.
- **Option D**: The histogram does not appear to depict a normal distribution. The frequencies generally increase and the histogram is roughly symmetric.
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