7. Chase and Devin began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Chase took a test in Math and earned a 77.8, and Devin took a test in Social Studies and earned a 69.6. Use the fact that all the students' test grades in the Math class had a mean of 73.9 and a standard deviation of 9.3, and all the students' test grades in Social Studies had a mean of 65.6 and a standard deviation of 10.6 to answer the following questions. a) Calculate the z-score for Chase's test grade. z= b) Calculate the z-score for Devin's test grade. z= c) Which person did relatively better?

• Chase
• Devin
• They did equally well.

9. A population of values has a normal distribution with =173.3 and =8.5 You intend to draw a random sample of size n=12

First calculate z, round it to two (2) decimal places, then use the rounded z-score to determine the required probability accurate to four (4) decimal places.

1. Find the probability that a single randomly selected value is less than 180.1. P(x<180.1)=
2. Find the probability that a sample of size n=12 is randomly selected with a mean less than 180.1. P(x<180.1)=

10. The number of trades (in thousands) completed daily by an online stock brokerage follows a normal distribution with a mean of 94.9 and a standard deviation of 28.8. On average, the brokerage receives $6.18 commission per trade. For samples of sizen=12

1. Determine the mean and standard deviation of the sampling distribution of the sample mean daily commissions received (in thousand dollars) accurate to 3 decimal places: a) Mean = thousand dollars b) Standard deviation = thousand dollars
2. Determine the following probabilities (as percentages) accurate to one (1) decimal place.

What is the probability that the mean daily commissions received is

1. a) less than $507,996? %% b) between $488,838 and $670,530? %%