Discuss the below:
Q1. The distribution of SAT scores is normal with µ=500 and σ=100.
a. What SAT score, x-value separates the top 15% of the distribution from the rest?
b. What SAT score. X-value separates the top 20% of the distribution from the rest?
c. What SAT score. X-value separates the top 25% of the distribution from the rest?
Q2. Over the past 10 years the local school district has measured physical fitness for all high school freshmen. During that time, the average score on a treadmill endurance task has been µ=19.8 minutes with a standard deviation of σ=7.2 minutes. Assuming that the distribution is approximately normal, find each of the following probabilities.
a. What is the probability of randomly selecting a student with a treadmill time greater than 25 minutes? In symbols, p(X>25)= ?
b. What is the probability of randomly selecting a student with a time greater than 30 minutes? In symbols, p(x>30) ?
c. If the school required a minimum time of 10 minutes for students to pass the physical education course, what proportion of the freshman would fail?
Q3. Rochester, New York, averages µ=21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ=6.5 inches. This year a local jewelry store is advertising a refund of 50% off all purchases made in December, if we finish the month with more than 3 feet (36 inches) of total snowfall. What is the probability that the jewelry store will have to pay off on its promise?