Question

question 14 of 20
which of the following is not true in finding p(z is greater than 1.61)? assume that the mean = 0 and sigma = 1. select all correct answers that apply.
select the correct response(s):
the z value is located on the right side of the mean.
the value of p(z > 1.61) is less than 1.
my answer is not listed among the given choices.
the shaded region or the area under the curve starts from the extreme left and passes over the mean.
the shaded region or the area under the curve starts somewhere in the middle of the first half of the curve.
the z value is located on the left side of the mean.
the shaded region or the area under the curve ends at the extreme right.
the shaded region or the area under the curve starts somewhere on the second half of the curve.
the value of p(z > 1.61) is more than 1.

Explanation:

1. For $P(z > 1.61)$ on a standard normal curve ($\mu=0, \sigma=1$):

• A positive z-score (1.61) lies right of the mean, so the claim it is left of the mean is false.
• The shaded region for $P(z > 1.61)$ starts at $z=1.61$ (right half of the curve) and extends to the extreme right. Claims that it starts at the far left, or in the first (left) half are false.
• All probabilities in a normal distribution are between 0 and 1, so $P(z > 1.61)$ cannot be greater than 1, making that claim false.
• The true statements (z right of mean, $P(z>1.61)<1$, shaded region starts in the second half/ends at extreme right) are excluded, as we identify untrue claims.

Answer:

The shaded region or the area under the curve starts from the extreme left and passes over the mean., The shaded region or the area under the curve starts somewhere in the middle of the first half of the curve., The z value is located on the left side of the mean., The value of P(z > 1.61) is more than 1.