Question

which of the following is true about the probability p(z is between -1.23 and < 0)? select all that apply.
select the correct response(s):
the upper bound goes beyond to the right of the mean.
my answer is not listed among the given choices.
the lower bound is on the first half of the curve.
the lower bound is not a very small number.
the upper bound is not a very large number.
the upper limit does not extend beyond the mean.
the area under the curve is more than 0.5.
the area under the standard normal distribution curve is less than 1.

Explanation:

Step1: Recall standard normal properties

For a standard normal distribution ($z$-distribution), the mean is $\mu=0$, the curve is symmetric about 0, and the total area under the curve is 1.

Step2: Analyze bounds

The interval is $-1.23 < z < 0$. The upper bound (0) is equal to the mean, so it does not go beyond the right of the mean, and it is not a very large number. The lower bound ($-1.23$) is left of the mean (first half of the curve) and is not an extremely small value (like $z < -3$).

Step3: Analyze area

The area between $-1.23$ and 0 is the area left of the mean (0.5) minus the area left of $-1.23$ (≈0.1093), so $\text{Area} = 0.5 - 0.1093 = 0.3907$, which is less than 0.5. Any partial area under the standard normal curve is less than the total area of 1.

Answer:

• The lower bound is on the first half of the curve.
• The lower bound is not a very small number.
• The upper bound is not a very large number.
• The upper limit does not extend beyond the mean.
• The area under the standard normal distribution curve is less than 1.