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# Basic Statistics Test 1

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Basic Statistics
Name:
Test 1

1) A test worth 100 points was given to a class with the following results:
Midpoint Interval Freq. Rel. Freq.
89.5 - 99.5 5
79.5 - 89.5 8
69.5 - 79.5 17
59.5 - 69.5 7
49.5 - 59.5 3

A) Fill in the Midpoint column and the Relative Frequency column in the above
table.

B) Draw the Histogram.

C) Calculate the population mean and population standard deviation.
___________ , _____________

D) What proportion of the class score 79.5 or above?
P(X 79.5) __________________

2) Consider the probability experiment of flipping a fair coin 6 times. Let X be the
number of heads. The probability distribution is given in the following table:
X P(X) freq.
0 .016 1
1 .094 6
2 .234 15
3 .313 20
4 .234 15
5 .094 6
6 .016 1

A) Carefully Draw the Histogram, labeling both axis.

B) Calculate the population mean and standard deviation.
___________ , _____________

C) What is the probability of flipping a coin 6 times and getting exactly 3 heads?
P(X 3) __________________

D) What is the probability of flipping a coin 6 times and getting 4 or MORE heads?
P(X 5) __________________
3) Emissions data for a sample of different vehicles are given for HC (hydrocarbon) and CO (carbon monoxide), which are both measured in grams per meter.

HC 0.65 0.55 0.72 0.83 0.57 0.51 0.43 0.37
CO 14.7 12.3 14.6 15.1 5.0 4.1 3.8 4.1

A) Construct the scatter diagram of the data.

B) Calculate the linear correlation coefficient r, and the slope and y-intercept of the regression line. Draw the graph of the regression line on the same plot as the scatter diagram above.
r =
slope =
y-intercept =

C) Find the best predicted value of CO given that the HC amount is 0.62 g/m.

4) Listed below are intervals (in minutes) between eruptions of the Old Faithful geyser in Yellowstone National Park. After each eruption, the National Park Service provides an estimate of the length of time to the next eruption. From the sample data below, find the mean and standard deviation for the time between eruptions.
98, 92, 95, 87, 96, 90, 65, 92, 95, 93, 98, 94, 77, 85, 81, 93

5) Stanford Binet IQ scores have a mean of 100 and a standard deviation of 15. Albert Einstein reportedly had an IQ of 160. Convert Einsteins's IQ score to a z score. Suppose Forrest Gump had an IQ score of 65. Convert Forrest Gump's IQ score to a z score.

Ans: Einstein's z score = _________ and Forrest Gump's z score = __________

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Basic Statistics
Name:
Test 1

1) A test worth 100 points was given to a class with the following results:
Midpoint Interval Freq. Rel. Freq.
89.5 - 99.5 5
79.5 - 89.5 8
69.5 - 79.5 17
59.5 - 69.5 7
49.5 - 59.5 3

A) Fill in the Midpoint column and the Relative Frequency column in the above
table.

Midpoint Interval Freq Rel Freq
94.5 89.5 99.5 5 0.125
84.5 79.5 89.5 8 0.2
74.5 69.5 79.5 17 0.425
64.5 59.5 69.5 7 0.175
54.5 49.5 59.5 3 0.075
40 1.00

B) Draw the Histogram.

C) Calculate the population mean and population standard deviation.

midpoint x f f*x f*x^2
94.5 5 472.5 44651.25
84.5 8 676 57122
74.5 17 1266.5 94354.25
64.5 7 451.5 29121.75
54.5 3 163.5 8910.75
sum 40 3,030.00 234,160.00 ...

Solution provided by:
###### Education
• MSc, California State Polytechnic University, Pomona
• MBA, University of California, Riverside
• BSc, California State Polytechnic University, Pomona
• BSc, California State Polytechnic University, Pomona
###### Recent Feedback
• "Excellent work. Well explained."
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• "Thank you so very much. This is very well done and presented. I certainly appreciate your hard work. I am a novice at statistics and it is nice to know there are those out there who really do understand. Thanks again for an excellent posting. SPJ"
• "GREAT JOB!!!"
• "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "

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