Question

the average daily jail population in the united states is 706,242. if the distribution is normal and the standard deviation is 52,145. find the probability that on a randomly selected day, the jail population is greater than 750,000? in this problem, which of the following statements is correct? select the correct response: the area that is of no interest to the problem solver is less than 0.5. the lower bound is -9e99. my answer is not listed among the given choices. the upper bound is -9e99. the area of interest is greater than 0.5. the lower bound is -9e-99. the z score is negative. the mean of the distribution is centered at 706,242.

Explanation:

Step1: Identify given values

Mean $\mu = 706,242$, standard deviation $\sigma = 52,145$, target value $x = 750,000$

Step2: Calculate z-score

$z = \frac{x - \mu}{\sigma} = \frac{750000 - 706242}{52145} \approx 0.84$

Step3: Analyze each option

1. Area of interest ($P(X>750000)$) corresponds to $z>0.84$, which is less than 0.5, so "The area of interest is greater than 0.5" is wrong.
2. The uninteresting area is $1 - P(X>750000) > 0.5$, so "The area that is of no interest to the problem solver is less than 0.5" is wrong.
3. The z-score is positive (~0.84), so "The z score is negative" is wrong.
4. For upper tail probability ($X>750000$), lower bound is 750000, upper bound is $+\infty$ (not -9E99), so upper/lower bound options are wrong.
5. The mean of the normal distribution is its center, so "The mean of the distribution is centered at 706,242" is correct.

Answer:

The mean of the distribution is centered at 706,242.