Normal Curve, z Scores, Probability, and Binomial Distribution

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PSYC4700 – Statistics for the Behavioral Sciences
u04a1 ? Normal Curve, z Scores, Probability,
and Binomial Distribution
Complete the following problems within the Word document (do not submit other
files). Show your work for problem sets that require calculations. Ensure your
answer to each problem is clearly visible. (You may want to highlight your answer
or use a different font color to set it apart.)
Submit the document to your instructor by Sunday, 11:59 p.m. central time.
Problem Set 4.1: Mutually Exclusive Outcomes
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Criterion: Determine if events are mutually exclusive.
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Instruction: Consider the following events. If the outcomes are mutually
exclusive, type yes. If the outcomes are not mutually exclusive, type no.
a. Turning right or turning left.
b. Studying Spanish or studying Italian.
c. Flipping heads on a coin or flipping tails on a coin.
d. Drawing an eight from a deck of cards or drawing a king from a deck of cards.
e. Riding a bike or wearing a hat.
Problem Set 4.2: Probabilities: Dichotomous Events
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Criterion: Calculate probability for a dichotomous event.
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Data: Jane has flipped a coin 10 times, and each time it has landed on
heads.
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Instruction: Answer the following:
o
What is the probability that Jane?s 11th flip will land on heads as well?
Problem Set 4.3: Calcuations on z and the Unit Normal Table
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Criterion: Calculate percentages based on z scores and the normal
curve.
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Data: For homes that were sold in the past year, the average number of days on
the market (DOM) was 266 days. During this time, DOM was normally
distributed, with a standard deviation of 12 days. The Carmichaels sold their
house in 245 days.
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Instruction: Using the unit normal table, answer what percentage of
homeowners:
a. Sold their home at the same point or earlier than the Carmichaels?
b. Sold their home at a later point than the Carmichaels?
c. Sold their home between 245 days and the average DOM?
(Assignment continues on next page.)
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PSYC4700 – Statistics for the Behavioral Sciences
Problem Set 4.4: Calculating z Scores in SPSS
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Criterion: Calculate z scores using SPSS.
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Data: The following is a list of the number of goals scored over a 10-game soccer
season:
2, 1, 5, 6, 0, 0, 3, 8, 1, 2.
Instructions: Complete the following steps:
a. Enter the data into SPSS using the variable name Goals.
b. In the Toolbar, click Analyze, select Descriptive Statistics, and then select
Descriptives.
c. Select Goals and then click Arrow to send data over to the right side of the table.
Check the box Save Standardized Values as Variables.
d. Select Options, check the boxes Mean and Standard Deviation, and then deselect
all other boxes. Click Continue.
e. Click OK and then copy and paste the descriptive statistics table below.
f. Go to the Data View in SPSS. You will see that the z scores have been added to the
file. Paste a screenshot of the Data View, showing the z scores, into the Word
document.
g. Which number of goals is closest to the z score of 0?
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Problem Set 4.5: Area and the Normal Curve
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Criterion: Calculate z scores and find the area under a normal curve.
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Data: The mean combined SAT score for a sample of high school seniors
is 1500 and the standard deviation is 250.
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Instructions: Answer the following:
a. What percentage of students scored below 1000?
b. What percentage of students scored above 1750?
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