Final answer:
To find the probability p(z < 2.12), use the z-table. The correct answer is a. 0.9830.
Step-by-step explanation:
To find the probability p(z < 2.12), we can use a standard normal distribution table or a calculator. In this case, we can use the z-table to find the area to the left of 2.12.
he student asked what the probability P(z < 2.12) is for a standard normal random variable z. To find this, one would use a standard normal distribution table, a calculator with statistical functions, or computer software capable of calculating normal probabilities.
Using such a table or tool will give you the area under the standard normal curve to the left of the z-score of 2.12. This area represents the cumulative probability. The correct answer from the options provided is closest to 0.9830, which means that approximately 98.30% of the data in a standard normal distribution falls to the left of a z-score of 2.12.
- First, locate 2.1 in the leftmost column of the z-table.
- Then, move to the column that corresponds to 0.02 (since 0.12 differs from 0.10 by 0.02).
- The intersection of the row and column gives us the area, which is approximately 0.9821.
Therefore, the correct option is a. 0.9830, as it is the closest value to 0.9821.