Answer:
THE ANSWER IS GIVEN BELOW
Step-by-step explanation:
To find the z-values corresponding to the bottom 40% of the standard normal distribution, we need to find the z-values for which 40% of the area under the curve lies below them. In other words, we're looking for the z-values that correspond to the 40th percentile.
We can use a standard normal distribution table or a statistical software to find these values.
Using a standard normal distribution table, we look for the value closest to 0.4000 (since standard normal tables typically provide values for the cumulative probability from the left tail). The closest value to 0.4000 is often found to be 0.4005 or 0.3997.
Alternatively, using statistical software, we can directly find the z-value corresponding to the 40th percentile. For example, in Python using the `scipy.stats` module:
```python
from scipy.stats import norm
z_value = norm.ppf(0.40)
print(z_value)
```
This would give us the z-value corresponding to the 40th percentile of the standard normal distribution.
Once we find the z-value, we can use it to find the corresponding standard deviation in terms of standard deviations from the mean (μ), as the standard normal distribution has a mean of 0 and a standard deviation of 1. These z-values represent the lower boundaries of the corresponding intervals in the standard normal distribution.