The weights of adult males are normally distributed with a mean of 172 lb and a standard deviation of 29 lb
Q.Find the weight that divides the upper 2% of weights from the lower 98%
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and it corresponding Z score. Use Z value to find score in the above equation.
To find the weight that divides the upper 2% of weights from the lower 98%, we need to determine the z-score associated with the 2nd percentile.
Step 1: Determine the z-score corresponding to the 2nd percentile.
The 2nd percentile is equivalent to the cumulative probability of 0.02. We can find the z-score using the Z-table or a calculator.
Using a Z-table:
- Look up the value of 0.02 in the z-table. The closest value is 0.02, which corresponds to a z-score of approximately -2.05.
Using a calculator:
You can use the inverse normal distribution function (also known as the quantile function) to find the z-score. For example, in Python, you can use the `scipy.stats` module:
```python
from scipy.stats import norm
# Find the z-score for cumulative probability 0.02
z_score = norm.ppf(0.02)
print(z_score)
```
The resulting z-score is approximately -2.05.
Step 2: Calculate the weight value corresponding to the z-score.
To calculate the weight value, we can use the formula:
Weight = Mean + (Z-score * Standard Deviation)
Weight = 172 + (-2.05 * 29)
Weight = 172 - 59.45
Weight ≈ 112.55 lb
Therefore, the weight that divides the upper 2% of weights from the lower 98% is approximately 112.55 lb.