91影视

Baseball salaries Brad Lidge played a crucial role as the Phillies鈥� 鈥渃loser,鈥� pitching the end of many games throughout the season. Lidge鈥檚 salary for the $2008$ season was $\$6,350,000$

(a) Find the percentile corresponding to Lidge鈥檚 salary. Explain what this value means.

(b) Find the z-score corresponding to Lidge鈥檚 salary. Explain what this value means.

Baseball salaries Did Ryan Madson鈥檚 , who was paid $\$1,400,000$, have a high salary or a low salary compared with the rest of the team? Justify your answer by calculating and interpreting Madson鈥檚 percentile and z-score.

Each year, about $1.5$million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was $46.9$and the standard deviation was$10.9$. Nationally, $5.2\%$of test takers earned a score of 65 or higher on the Critical Reading test鈥檚 $20$to $80$scale.9

PSAT scores Scott was one of $50$junior boys to take the PSAT at his school. He scored $64$on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all $50$boys鈥� Critical Reading scores, the mean was $58.2$and the standard deviation was $9.4$

(a) Write a sentence or two comparing Scott鈥檚 percentile among the national group of test-takers and among the $50$boys at his school.

(b) Calculate and compare Scott鈥檚 z-score among these same two groups of test-takers.

Each year, about $1.5$million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was $46.9$and the standard deviation was $10.9$Nationally, $5.2\%$ of test-takers earned a score of $65$ or higher on the Critical Reading test鈥檚 $20$ to $80$ scale. 9

PSAT scores How well did the boys at Scott鈥檚 school perform on the PSAT? Give appropriate evidence to support your answer.

Tall or short? Mr. Walker measures the heights (in inches) of the students in one of his classes.

He uses a computer to calculate the following numerical summaries: Next, Mr. Walker has his entire class stand on their chairs, which are $18$ inches off the ground. Then he measures the distance from the top of each student鈥檚 head to the floor.

(a) Find the mean and median of these measurements. Show your work.

(b) Find the standard deviation and IQR of these measurements. Show your work.

Old folks Here is a stem plot of the percent of residents aged $65$ and older in the$50$states:

(a) Find and interpret the percentile for Colorado, which has $10.1\%$of its residents aged $65$or older.

(b) Find and interpret the percentile for Rhode Island, with $13.9\%$of residents aged $65$or older.

(c) Which of these two states is more unusual? Explain.

Paul is$15$years old and $179$cm tall.

(a) Find the z-score corresponding to Paul鈥檚 height. Explain what this value means.

(b) Paul鈥檚 height puts him at the$85th$ percentile among $15$-year-old males. Explain what this means to someone who knows no statistics.

T2.2. For the Normal distribution shown, the standard deviation is closest to

(a) 0

(b) 1

(c) 2

(d) 4

(e) 5

Teacher raises A school system employs teachers at salaries between $\backslash (28,000$ and $\backslash )60,000$. The teachers鈥� union and the school board are negotiating the form of next year鈥檚 increase in the salary schedule.

(a) If every teacher is given a flat $\backslash (1000$ raise, what will this do to the mean salary? To the median salary? Explain your answers.

(b) What would a flat$\backslash )1000$ raise do to the extremes and quartiles of the salary distribution? To the standard deviation of teachers鈥� salaries? Explain your answers.

Lynette, a student in the class, is $65$ inches tall. Find and interpret her z-score.