Answer :
To solve this problem, you need to determine which value out of 0.02, 0.14, 0.34, and 0.84 corresponds to a particular z-score using the given probabilities.
Let's analyze the provided table first:
[tex]\[ \begin{array}{|c|c|} \hline z & \text{Probability} \\ \hline 0.00 & 0.5000 \\ \hline 1.00 & 0.8413 \\ \hline 2.00 & 0.9772 \\ \hline 3.00 & 0.9987 \\ \hline \end{array} \][/tex]
This table shows standard normal distribution probabilities, where 'z' is the z-score and the associated probability is the cumulative probability from the left up to that z-score.
Now, let's interpret the probabilities for the given choices:
[tex]\[ \begin{array}{c} 0.02 \\ 0.14 \\ 0.34 \\ 0.84 \\ \end{array} \][/tex]
Out of these probabilities, our task is to find the value that would best fit into this context.
- 0.02: This is a small probability, likely corresponding to a z-score significantly below 0.
- 0.14: This probability is closer to what you might expect for a slightly negative z-score.
- 0.34: This probability might correspond to a slightly positive z-score but lower than 1.
- 0.84: This probability is very close but not exactly matching 0.8413 (which corresponds to a z-score of 1).
Looking at these options, our best match, and thus our correct interpretation, would be 0.14 as it effectively matches a point where the cumulative probability in the standard normal distribution indicates a certain z value.
Thus, the final correct value from our provided choices is:
[tex]\[ \boxed{0.14} \][/tex]
Let's analyze the provided table first:
[tex]\[ \begin{array}{|c|c|} \hline z & \text{Probability} \\ \hline 0.00 & 0.5000 \\ \hline 1.00 & 0.8413 \\ \hline 2.00 & 0.9772 \\ \hline 3.00 & 0.9987 \\ \hline \end{array} \][/tex]
This table shows standard normal distribution probabilities, where 'z' is the z-score and the associated probability is the cumulative probability from the left up to that z-score.
Now, let's interpret the probabilities for the given choices:
[tex]\[ \begin{array}{c} 0.02 \\ 0.14 \\ 0.34 \\ 0.84 \\ \end{array} \][/tex]
Out of these probabilities, our task is to find the value that would best fit into this context.
- 0.02: This is a small probability, likely corresponding to a z-score significantly below 0.
- 0.14: This probability is closer to what you might expect for a slightly negative z-score.
- 0.34: This probability might correspond to a slightly positive z-score but lower than 1.
- 0.84: This probability is very close but not exactly matching 0.8413 (which corresponds to a z-score of 1).
Looking at these options, our best match, and thus our correct interpretation, would be 0.14 as it effectively matches a point where the cumulative probability in the standard normal distribution indicates a certain z value.
Thus, the final correct value from our provided choices is:
[tex]\[ \boxed{0.14} \][/tex]
