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APPLICATIONS of NORMAL DISTRIBUTION 1.) Scores on a test can be approximated with a normal distribution. If the average score was an 86 and the standard deviation was 3, find the probability that a randomly chosen test has a score... a.) below 80: b.) between 80 and 90: c.) greater than 90: d.) If 2,000 people took this test, how many can be expected to score greater than a 95? 2.) A test is given to government employees. Historically, the scores have been approximately normal with / =75 and o =6. If an employee scores less than 64 on this test, regulations state that he or she cannot be hired. Suppose 800 applicants take this test. Estimate the number who will not be hireable: 3.) A study found that the mean yearly migration distance of the green turtle was 2400 kilometers and the standard deviation was 525 kilometers. Additionally, the study found that the migration distances of this turtle were approximately normal in distribution. Find the probability that a randomly selected green turtle has a yearly migration distance of... a.) less than 1800 km: b.) between 1900 and 2500 km : c.) greater than 2200 km: d.) According to this data, approximately 95% of green turtles migrate less than km per year. [ Round to the nearest km.] 4.) Systolic blood pressure readings in a particular population are approximately normal with a mean of 117 mb. and o =5 mb. A researcher wishes to select people for a study but wants to exclude those whose systolic readings are either in the top 10% and bottom 10%. Therefore, he should only include people whose readings are between and 5.) On a Statistics final exam, the grades were approximately normal in distribution with a mean of 80 and o =4. 650 students took the final. Use this data and the table to the right to estimate answers to the following questions: Grade Score range A 90 or above B [80-90) C [70 - 80) Fail Below a 70 a.) About how many exams received an A grade? b.) About how many exams received a B grade? c.) About how many exams received a passing grade? d.) Now suppose that the Professor wants to "curve" the test and give an "A" grade to the top 50 exams. What is the lowest score that would qualify for an "A" under this new grading scheme