The population mean and standard deviation

(1) Find the z score 0.4744______________ 0.4744

(2) The weight of the bags of carrots are normally distributed with a mean of 34 ounces and a standard deviation of 3.5 ounces. Bags in the upper 4.5% are too heavy and must be repackaged. What is the most a bag of baby carrots can weigh and not need to be repackaged.

(3) In a large section of a statistics class the points for the final exam are normally distributed with a mean of 76 and a standard deviation of 9. Grades are assigned such that the top 10% receive A’s, the next 20% received B’s, the middle 40% receive C’s, the next 20% receive D’s and the bottom 10% receive F’s. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D.

(4) The population mean and standard deviation are given below. Find the required probability and determine whether the sample mean will be considered unusual, why or why not. For a sample of N=75, the probability of a sample mean being greater than 212 if mean = 211 and standard deviation = 3.7. Would the given sample be considered unusual?

Sample Solution

ven though neuroscience has developed immensely throughout the years, predicting criminal behavior through scans can produce a reverse-inference error. “The reverse-inference error is especially prevalent in the interpretation of brain activity in functional neuroimaging studies” (Choi). As previously stated, the reliance of electroencephalogram data may show the activity within the brain, but depending on the section, the brain may be overactive during such time. When looking at an individual’s amygdala that is characterized as abnormal and overactive can be argued to the point of reverse-inference error due to trying to distinguish what is a normal or abnormal sign of the brain’s fear center (Choi).

Brain Scans Versus Self-Report:

Brain scans provide more complexity to detect brain impairments in individuals despite a clinical psychologist’s findings. A common problem within neurolaw is the group to individual inference problem. Psychologists often identify associations of brain defects with impairments by comparing a group of subjects with a localized defect to a group of subjects without the defect; this can result in overlapping due to the idea that impaired patients may have better control over a specific area in regard to the healthy controls and vice versa (Choi).

The issue with psychological based evidence is that very few neuroimaging-based tests are used in psychiatric diagnosis which lacks the sufficient sensitivity and specificity to be reliable enough for inclusion in diagnostic criteria” (Choi). When looking at the defendants self-reporting of their behavior, brain scans often reveal more than those reports suggest. “While most people’s self-reports are not very accurate, they do not realize their self-reports are wrong so often in predicting future behavior. The brain seems to reveal something important that we may not even realize” (University of California).

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