Find the number z that satisfies the proportion of the observations in a standard normal distribution less than z is 30%?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.30) and its related Z score.
To find the number z that satisfies the proportion of the observations in a standard normal distribution less than z is 30%, you can follow these steps:
1. Look up the value of the cumulative probability in a standard normal distribution table: Since the given proportion is less than z, you need to find the value that corresponds to a cumulative probability of 0.30.
2. Use the standard normal distribution table or a statistical calculator to find the z-score associated with a cumulative probability of 0.30. Look for the closest value in the table that is less than 0.30. In this case, the closest value is 0.3106, which corresponds to a z-score of approximately -0.52.
Therefore, the number z that satisfies the proportion of observations in a standard normal distribution less than z is 30% is approximately -0.52.