Answer :
The missing z-score corresponds to the positive z-value since the shaded area is to the right of the mean. Given that the standard normal distribution is not symmetric, we use the symmetry property to find the z-score. Therefore, the missing z-score is[tex]\(\boxed{\text{d) } 0.96}\).[/tex]
Calculate the missing z-score:
Given:
Shaded area = 0.4609
Given z-score = 0.06
First, we find the complementary area:
Complementary area = 1 - Shaded area = 1 - 0.4609 = 0.5391
Next, we find the z-score corresponding to the complementary area. We consult a standard normal distribution table or use a calculator to find the z-score corresponding to the cumulative probability of 0.5391.
Upon calculation, we find the z-score corresponding to the cumulative probability of 0.5391 is approximately 0.96.
Since the given z-score is positive (0.06), the missing z-score should also be positive.
Therefore, the missing z-score is 0.96.
To find the missing z-score, we begin by determining the complementary area to the shaded region in the standard normal distribution. Since the shaded area is given as 0.4609, we subtract this value from 1 to obtain the complementary area, which is 0.5391.
Next, we locate the z-score corresponding to this complementary area using a standard normal distribution table or a calculator. The z-score corresponding to the cumulative probability of 0.5391 is approximately 0.96.
Given that the given z-score is positive (0.06), we infer that the missing z-score should also be positive. Therefore, the missing z-score is 0.96. This process involves understanding the relationship between cumulative probabilities and z-scores in the standard normal distribution, allowing us to find the missing z-score accurately.
It highlights the importance of utilizing statistical tools and concepts to analyze and interpret data effectively in various fields such as finance, science, and engineering.
