Chapter 6-(6.1 and 6.2) Assignment: (Use PhStat) 25 Points
1. (3 pts) The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes. What is the probability that a randomly selected exam will require less than 20 minutes to grade?
A) 0.8108 B) 0.3715 C) 0.6328 D) 0.9230
2. (3 pts) Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?
A) 0.5274 B) 0.2650 C) 0.1548 D) 0.3875
3. (4 pts) Suppose you can buy either battery A or battery B. The lifetime of battery A can be modeled with a normal distribution with mean=12 hours and standard deviation=8 hours. The lifetime of battery B can be modeled with a normal distribution with mean=8 hours and standard deviation=1 hour. Suppose you can only buy one battery, and you need to use it to power your grandmother’s life-support respirator for 7 hours. If the battery dies, so does your grandmother (and you really, really love your grandmother and you don’t want her to die). Which battery gives your grandmother the best shot at survival (Hint: use normal dist.)? Why? Show your work using appropriate probability calculations.
4. (6 pts) Ithaca, New
York gets an average of 35.4” of rain each year with a standard deviation of
4.2”. Assume the
a. What percentage of years does Ithaca get more than 40” of rainfall?
b. What rainfall amount separates the “driest” 20% of years from the “wettest” 80%?
5. (3 pts) The numbers of monthly cell phone minutes used by students at one university are normally distributed with a mean of 110 minutes and standard deviation of 33 minutes. What is the third quartile for cell phone usage at this university?
6. (3 pts) A local firehouse receives on average 45 calls per week with a standard deviation of 6 calls. Suppose that the firefighters are anticipating an unusually busy week How many calls should they prepare for if they anticipate that this week will be busier than 85% of their weeks?
7. (3 pts) Scores on a midterm exam are normally distributed with a mean of 73 and a standard deviation of 9 points. What score is at the 90th percentile?