1. In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean = 570 and standard deviation = 145.

a. Calculate the z-score for an SAT score of 520. Interpret it using a complete sentence.

b. What math SAT score is 1.8 standard deviations above the mean? What can you say about this SAT score?

c. For 2012, the SAT math test had a mean of 414 and a standard deviation of 107. The ACT math test is an alternative to the SAT and is approximately normally distributed with a mean of 23 and a standard deviation of 5.7. If one person took the SAT math test and scored 620 and a second person took the ACT math test and scored 32, who did better with respect to the test they took?

2.A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is traveling at more than 100 km/hr?

3.For a certain type of computer, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.

4.Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university?

5.In the 1992 presidential election, Alaska's 70 election districts averaged 1,656.8 votes per district for President Clinton.

The standard deviation was 372.3. (There are only 70 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X = number of votes for President Clinton for an election district.

a. State the approximate distribution of X.

b. Is 1,656.8 a population mean or a sample mean? How do you know?

c. Find the probability that a randomly selected district had fewer than 1,500 votes for President Clinton. Sketch the graph and write the probability statement.

d. Find the probability that a randomly selected district had between 1,600 and 1,720 votes for President Clinton.