Question

given the figure below, which of the following statements is not true?
select the correct response:
the upper bound is a very large number.
the mean lies on the 50th percentile.
the area of interest is greater than 0.5.
the upper bound is 9e99.
the shaded region or the area of interest is more than 50%.
the z score lies to the right side of the mean.
the lower bound is less than zero.
the value of the z score is positive.
my answer is not listed among the given choices.

Explanation:

Step1: Analyze the normal curve

The mean is at $z=0$. The shaded region starts at a $z$ value left of 0, so this $z$ is negative.

Step2: Evaluate each statement

• "The upper bound is a very large number.": True (normal curve extends to $+\infty$, often represented as a large number like 9E99).
• "The mean lies on the 50th percentile.": True (mean of normal distribution is the 50th percentile).
• "The area of Interest is greater than 0.5.": True (given area is 0.8962 > 0.5).
• "The upper bound is 9E99.": True (standard representation for $+\infty$ in stats software).
• "The shaded region or the area of Interest is more than 50%.": True (0.8962 = 89.62% > 50%).
• "The z score lies to the right side of the mean.": False (the $z$ is left of 0, the mean).
• "The lower bound is less than zero.": True (the $z$ is left of 0, so < 0).
• "The value of the z score is positive.": False (the $z$ is left of 0, so negative).

Answer:

The z score lies to the right side of the mean.
The value of the z score is positive.