Answer :
To answer this question, we need to find the probabilities corresponding to the given z-scores using the provided table. Here is a step-by-step solution for each z-score:
1. For z = 0.02:
The closest z-score in the table to 0.02 is 0.00. The corresponding probability for [tex]\( z = 0.00 \)[/tex] is 0.5000. Therefore, the probability for [tex]\( z = 0.02 \)[/tex] is approximately 0.5000.
2. For z = 0.14:
The closest z-score in the table to 0.14 is 0.00 as well since 0.14 is closer to 0.00 than to any other values in the table. Thus, the corresponding probability for [tex]\( z = 0.00 \)[/tex] is 0.5000. Hence, the probability for [tex]\( z = 0.14 \)[/tex] is approximately 0.5000.
3. For z = 0.34:
The closest z-score in the table to 0.34 is still 0.00 since 0.34 is closest to 0.00 compared to other available values in the table. Therefore, the probability for [tex]\( z = 0.34 \)[/tex] is approximately 0.5000.
4. For z = 0.84:
The closest z-score in the table to 0.84 is 1.00. The corresponding probability for [tex]\( z = 1.00 \)[/tex] is 0.8413. Hence, the probability for [tex]\( z = 0.84 \)[/tex] is approximately 0.8413.
Thus, the probabilities corresponding to the given z-scores in the order of [tex]\( 0.02, 0.14, 0.34, \)[/tex] and [tex]\( 0.84 \)[/tex] are:
[tex]\[ \begin{aligned} &\text{Probability for } z = 0.02 &\approx 0.5000 \\ &\text{Probability for } z = 0.14 &\approx 0.5000 \\ &\text{Probability for } z = 0.34 &\approx 0.5000 \\ &\text{Probability for } z = 0.84 &\approx 0.8413 \end{aligned} \][/tex]
So, the final result is [tex]\([0.5, 0.5, 0.5, 0.8413]\)[/tex].
1. For z = 0.02:
The closest z-score in the table to 0.02 is 0.00. The corresponding probability for [tex]\( z = 0.00 \)[/tex] is 0.5000. Therefore, the probability for [tex]\( z = 0.02 \)[/tex] is approximately 0.5000.
2. For z = 0.14:
The closest z-score in the table to 0.14 is 0.00 as well since 0.14 is closer to 0.00 than to any other values in the table. Thus, the corresponding probability for [tex]\( z = 0.00 \)[/tex] is 0.5000. Hence, the probability for [tex]\( z = 0.14 \)[/tex] is approximately 0.5000.
3. For z = 0.34:
The closest z-score in the table to 0.34 is still 0.00 since 0.34 is closest to 0.00 compared to other available values in the table. Therefore, the probability for [tex]\( z = 0.34 \)[/tex] is approximately 0.5000.
4. For z = 0.84:
The closest z-score in the table to 0.84 is 1.00. The corresponding probability for [tex]\( z = 1.00 \)[/tex] is 0.8413. Hence, the probability for [tex]\( z = 0.84 \)[/tex] is approximately 0.8413.
Thus, the probabilities corresponding to the given z-scores in the order of [tex]\( 0.02, 0.14, 0.34, \)[/tex] and [tex]\( 0.84 \)[/tex] are:
[tex]\[ \begin{aligned} &\text{Probability for } z = 0.02 &\approx 0.5000 \\ &\text{Probability for } z = 0.14 &\approx 0.5000 \\ &\text{Probability for } z = 0.34 &\approx 0.5000 \\ &\text{Probability for } z = 0.84 &\approx 0.8413 \end{aligned} \][/tex]
So, the final result is [tex]\([0.5, 0.5, 0.5, 0.8413]\)[/tex].
