1. Find each of the requested values for a population with a mean of $?=40$, and a
standard deviation of $?=8$
A. What is the z-score corresponding to $X=52?$
B. What is the X value corresponding to $z=-0.50?$
C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores?
D. What is the z-score corresponding to a sample mean of $M=42$ for a sample of $n=4$ scores?
E. What is the z-scores corresponding to a sample mean of $M=42$ for a sample of $n=6$ scores?
2. True or false:
a. All normal distributions are symmetrical
b. All normal distributions have a mean of 1.0
c. All normal distributions have a standard deviation of 1.0
d. The total area under the curve of all normal distributions is equal to 1
3. Interpret the location, direction, and distance (near or far) of the following zscores: $a.-2.00b.1.25c.3.50d.-0.34$
4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $\mu =78$ and $\sigma =12$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $82,74,62,68,79,94,90,81,80$.
5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $\$12(\mu =42,\sigma =12)$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the $\alpha =0.05$ level of significance.