Math Core

This test covers variables and frequency tables, displays of categorical and quantitative data, describing distributions with SOCS, summary statistics, box plots and outliers, comparing distributions, and the normal distribution.

Question 1

A survey records four variables for each student: the area code of the student's phone number, the number of AP courses the student is taking, the minutes the student spent on homework last night, and the student's favorite subject. How many of these four variables are categorical?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

In a random sample of $160$ registered voters, $52$ said they support a proposed transit tax. What is the relative frequency of supporters? Give a decimal.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 3

At School P, $45$ of $180$ students play a musical instrument. At School Q, $60$ of $300$ students do. By how many percentage points is the higher school's rate greater than the lower school's?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

The histogram shows the times, in minutes, that $50$ runners took to finish a $5$ km race. What percent of the runners took $35$ minutes or longer?

Finishing times of 50 runners (minutes)

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

The stemplot shows the scores of $23$ students on a chemistry exam. Which best describes the shape of the distribution?

Stem	Leaves
3	7
4
5	2 8
6	1 5 7
7	0 3 4 6 8 9
8	1 2 3 4 5 6 8
9	0 1 2 4

Key: $7 \mid 3$ means a score of $73$ .

Question 6

A histogram of the weights of all the dogs at a large dog show has two clear peaks, one near $15$ pounds and one near $65$ pounds. Which is the best description and explanation?

Question 7

Find the sample standard deviation $s_x$ of the values $2, \ 5, \ 6, \ 9, \ 13$ . Round to the nearest hundredth.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 8

The prices of items in an online store have mean $40 and standard deviation $8. The store raises every price by $10\%$ (multiplying by $1.1$ ) and then adds a $2 handling fee to each item. What is the new standard deviation of the prices, in dollars?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

How many values in this data set are outliers by the $1.5 \times \text{IQR}$ rule?

31, \ 44, \ 46, \ 47, \ 49, \ 50, \ 52, \ 53, \ 55, \ 56, \ 58, \ 60, \ 79

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

The box plot summarizes the weights of students' backpacks at a middle school. Which statement is supported by the plot?

Backpack weights (pounds)

Question 11

A gardener grew plants with and without a new fertilizer. The box plots show the plants' heights after six weeks. Which conclusion is best supported?

Plant height after six weeks (cm)

Question 12

The weights of a breed of cat are approximately normal with mean $10$ pounds and standard deviation $1.5$ pounds. Use the empirical rule to find the percent of these cats that weigh more than $13$ pounds.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

The lengths of bolts from a factory are approximately normal with mean $12$ cm and standard deviation $0.4$ cm. What proportion of bolts are shorter than $11.5$ cm? (Under the standard normal curve, the area to the left of $z = 1.25$ is $0.8944$ .) Give a decimal to four places.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 14

Scores on a state exam are approximately normal with mean $80$ and standard deviation $6$ . What score is at the $80$ th percentile? (The z-score with an area of $0.80$ to its left is about $0.84$ .)

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

Jamal's height is at $z = 1.2$ among the boys in his class, and Rosa's height is at $z = 0.9$ among the girls in her class. Which statement must be true?