For problems 1-5, standardize the value according to the given average and SD.
1. x = 10, average = 5 and SD = 2.
2. x = 73, average = 69 and SD = 3.
For problems 6-10, unstandardize the value according to the given average and SD.
3. z = -2.3, average = 160 and SD = 20.
4. z = 3.1, average = 2 and SD = 0.1.
5. To what value does the average always standardize?
For problems 12-16, find the area under the standard normal curve corresponding to the given range.
6. z between 1.2 and 1.8
7. z greater than 0.4
8. Attendance for a high school's football games is approximately normal, with an average attendance per game of 1,000 fans and an SD of 200. If the school charges $10 per ticket, about what percentage of the time does the school have a revenue of more than $12,500?
9. The times that the city bus arrives at a certain apartment complex each morning are approximately normally distributed, with an average time of 7:30 AM and a standard deviation of 10 minutes.
a) About what percentage of the time will the bus arrive between 7:25 and 7:35?
b) About what percentage of the time will the bus arrive between 7:15 and 7:45?
c) If you want to have a 95% certainty that you will catch the bus (that is, you arrive before the bus does), what time should you arrive at the stop?
d) 90% of the time, the bus will arrive no later than _________.
10. Final exam scores for a college statistics class were approximately normally distributed, with an average of 72% and an SD of 8%.
a) About what percentage of the class got better than an 80%?
b) About what percentage of the class got less than a 60%?
c) One student scored an 87%. What percentile rank did he have in the class?
d) Find the 75th percentile score for the test.