1. Suppose the mean SAT score for a students admitted to a university is 1000, with a standard deviation of 200. Suppose that a student is selected at random. If the scores are normally distributed, find the probability (percentage) that the student's SAT score is

Between 1000 and 1400

Between 1200 and 1400.

greater than 1400.

2.) The average height of 2000 women in a random sample is 64 inches. The standard deviation is 2 inches. The heights have a normal distribution.

How many women in the sample are between 62 and 66 inches tall?

How many women in the sample are between 60 and 68 inches tall?

How many women in the sample are between 58 and 70 inches tall?

3.) Records show that he average life expectancy of a pair of shoes is 2.2 years with a standard deviation of 1.7 years. A manufacturer guarantees that shoes lasting less than a year are replaced free. For every 1000 pairs sold, how many pairs should the manufacturer expect to replace free? Assume a normal distribution.

4.) The attendance over a weekly period of time at a movie theater is normally distributed with a mean of 10,000 and a standard deviation of 1000 persons. Find the percent of attendance figures that differs from the mean by 1500 persons or more.

5.) Spread of disease On a college campus of 10,000 students, a single student returned to campus infected by a disease. The spread of the disease through the student body is given by y= 10,000/ 1+999e^-0.99t
, where y is the total number infected at time t (in days). The school will shut down if 45% of the students are ill. What value of t corresponds to this percentage?