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Use the given shaded area (0.4609) in the middle of the standard normal distribution and the given z-score (0.06) to find the missing z-score. The shaded region is not symmetric about z = 0.

a) -1.69
b) 1.69
c) -0.96
d) 0.96

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.

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