Practice problems for homework 3

For pregnancies, assume mux = 280.6 days and sigmax = 9.7 days.

a. What is the z-score for 273 days?
b. What is the proportion that corresponds to 273 days?
c. What is the z-score for 288 days?
d. What is the proportion that corresponds to 288 days?
e. What proportion of pregnancies last between 273 to 288 days?





With the Central Limit Theorem, we need to know the average and standard deviation of a population and the average and size of a sample, x-bar and n, respectively. This gives us a z-score which corresponds to a proportion.

f. What is the z-score for 273 days for a sample where n = 8?
g. What is the proportion that corresponds to 273 days for a sample where n = 8?
h. What is the z-score for 288 days for a sample where n = 8?
i. What is the proportion that corresponds to 288 days for a sample where n = 8?
j. What proportion of pregnancies last between 273 to 288 days for a sample where n = 8?

Consider the following data set.

17, 19, 19, 18, 19, 19, 15, 20, 20, 20, 20, 14, 18, 20, 19, 20, 18, 19, 20, 16

Find the frequencies and relative frequencies for each value.

Answers in the comments.

Answers to quiz from 9/11

(10 points) On any single section of the SAT, mux = 500 and sx = 100. Find the z-scores for the following raw SAT scores and use the look-up table to find what proportion of the people taking the SAT will get a score that is less than or equal to the given score. Z-scores should be rounded to two places after the decimal and the proportions from the table are written to four decimal places.

SAT score: 570
z-score = .7
proportion at that z-score or less = .7580

SAT score: 750
z-score = 2.5
proportion at that z-score or less = .9938

SAT score: 395
z-score = -1.05
proportion at that z-score or less = .1469

SAT score: 625
z-score = 1.25
proportion at that z-score or less = .8944

SAT score: 490
z-score = -0.1
proportion at that z-score or less = .4602


(6 points) For the following movie studios find the average number of theaters on the opening weekend for the movies they made that were in the top 25 grossing movies of 2009 and find the median number of theaters of those sets of films. Round the answers to the nearest tenth.


Fox
Average number of theaters 3771.5
Median number of theaters 3898
Numbers on list: 3452, 3700, 4099, 4099, 4096, 3183


Sony
Average number of theaters 3298.5
Median number of theaters 3274
Numbers on list: 3404, 3144, 3527, 3119

WB
Average number of theaters 3572
Median number of theaters 3530
Numbers on list: 4325, 3269, 3110, 3626, 3530
(1 point each)
What movie had the biggest opening weekend?
The Twilight Saga: New Moon

What month had the most opening days on the list?
May (6)

What movie on the list opened earliest in the year?
Paul Blart: Mall Cop, Jan. 16

What movie on the list opened latest in the year?
Sherlock Holmes, Dec. 25

Practice problems for homework 2

Find the following statistics following set of data. Round all answers to two place after the decimal, except the proportions, which are given on the table to four places after the decimal

z(x) = (x - x-bar)/sx

17.41, 18.22, 19.17, 17.87, 18.15, 17.86, 18.12, 17.97, 18.46, 18.14

x-bar = ______

sx = _______

z(high) = _____ Proportion associated = ______

z(low) = _____ Proportion associated = _______

For the following movie studios, find the average opening weekend for the movies that were in the total opening weekend receipts for the same films. Round the answers to the nearest million dollars.

Average opening weekend for Fox: _________

Total opening weekend for Fox: ___________


Average opening weekend for WB: _________

Total opening weekend for WB: ___________


Average opening weekend for BV: _________

Total opening weekend for BV: ___________


Answers in the comments.

Answers to quiz from 9/6

Consider the total gross variable of the top 25 movies from 2009 (numbers on the blue sheet).
(12 points) Find the following statistics. Round all answers to the nearest million dollars. Don’t forget the dollar signs.

high = $749,000,000
Q3 = $268,000,000
Q2 (or median) = $180,000,000
Q1 = $146,000,000
low = $121,000,000
IQR = Q3 – Q1 = $122,000,000
High outlier threshold = $451,000,000
Low outlier threshold =-$37,000,000

Is there any outlying data and if so, what is it? Answer: Yes, Avatar at $749,000,000 is an outlier.


(8 points) The data set below is written in stem and leaf form.

14|3
13|
12|
11|
10|8
_9|
_8|5
_7|1578
_6|248
_5|559
_4|23569
_3|002448
_2|5

Find the following statistics. Round any decimal number to the nearest tenth.

n = 25
High = 143
Q3 = 73
Q2 = 55
Q1 =36
Low = 25
x-bar = 57.9
mode = 30, 34, 55

Reminders for this week.

1. Homework is due by noon on Friday. You can turn it in to my mailbox in the math lab G-201 or you can send it by e-mail to mhubbard@peralta.edu. If you turn it in electronically, you should print out a copy for your own records. I'll be handing out a copy of the correct answers to the people who turn it in online with marks indicating where the differences are.

2. YOU MUST HAVE A CALCULATOR BY THE NEXT CLASS PERIOD. Mark and I will be showing people how to input data sets using the TI-83/84 style calculators as well as the TI-30XIIs and other calculators people may have.

3. See you on Saturday. Send any questions you have to mhubbard@peralta.edu.

Practice problems for homework 1

1) Here are the homicide numbers for Oakland, Richmond and San Francisco from earlier in this century.

Oakland: 96 homicides, 399,000 population
Richmond: 40 homicides, 99,000 population
San Francisco: 96 homicides, 775,000 population

Find the murder rates from these years, rounded to the nearest tenth per 100,000 population and rank them from lowest (1st) to highest (3rd).

2) Here is a list of numbers. It is the number of wins by teams in the American League at the end of the 2008 regular season.

97, 95, 89, 86, 68, 89, 88, 81, 75, 74, 100, 79, 75, 61


a) Make a stem and leaf plot for the data.
b) Find the five number summary
c) Find IQR and the high and low outlier thresholds
d) Is there any outlying data?
e) find the average, rounded to the nearest tenth.

Answers in the comments.

Link to data on Box Office Mojo website (top 100 movies of 2008)

The following link will take you to a data set we will put into an Excel spreadsheet.

The top 100 box office movies of 2008