Statistics questions. Determining probabilities and z scores. Please help with all questions

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For each of the following problems, choose if a researcher should use a z for an individual score or a z for a sample mean. Just choose which statistic is appropriate. Do not compute the 2 yet.

o 17. A school psychologist wants to identify students who may need extra help in their math course and so gives the students a standardized math test. The scores are normally distributed and have a mean of 500 and a standard deviation of 100. Students who score below 400 are given additional tutoring. What percentage of students would you expect to receive scores at or below 400? Choose the correct statistic. 1. z for an individual score 2. z for a sample mean 0 18. A car seat manufacturer develops a seat that is safest for people who are between 62 inches and 68.5 inches. If the average height of women in the United States is 64 inches with a standard deviation of 2 inches, what percentage of women fall outside of the safest range? Choose the correct statistic. 1. z for an individual score 2. z for a sample mean

. 19. A researcher knows that poverty is often associated with poor nutrition. The researcher wants to determine if poverty is also related to

height. To test this association, he obtains a sample of25 women who have incomes below the poverty line. Assuming that the average height of women is 64 inches with a standard deviation of 2 inches, what is the probability that sampling error would result in obtaining a sample mean that is below 63 inches for a sample of 25 women? Choose the correct statistic. 1. z for an individual score 2. z for a sample mean . 20. The average worker in a manufacturing plant produces 27 units every hour with a standard deviation of 2.9. The manager of the plant took a sample of 25 workers and gave them special training designed to increase their productivity. After the special training was complete, the25 workers produced 28.2 units every hour. What is the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher? Choose the correct statistic. 1. z for an individual score 2. z for a sample mean

. 21. The manager of the manufacturing plant is responsible for distributing bonuses based on each worker's productivity. The mean productivity for all workers in the plant is 27 units per hour with a standard deviation of 2.9. The manager wants to give every worker in the top third a $200 bonus and every worker in the middle third a $100 bonus. The workers in the bottom third will get no bonus. What is the number of units produced per hour that separates those in the top third from those in the middle third? What is the number of units produced per hour that separates those in the middle third from those in the bottom third? (Hint: To do this problem, you ﬁrst need to ﬁnd the z scores with 1/3 (.333) of the scores in the tail. Then, you need to solve for X.) Choose the correct statistic. 1. z for an individual score 2. z for a sample mean

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