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Vesalius College
Midterm Exam
Course Title: Introduction to Statistics
Course Code: STA101
Time allowed: 80 minutes
Spring 2013
Professor: Luc Hens
Instructions:
– Store cell phones and any other electronic devices in your bags or coat
pockets, outside of your reach. Possession of any such item on your person
or place will be considered as evidence of cheating.
– If necessary, go to the bathroom before you start the exam. During the
exam, you cannot go to the bathroom or leave the classroom for another
reason.
– Remain seated during the last 15 minutes of the exam and wait until the
completion of the exam session. If you finish the exam before the final 15
minutes, they are permitted to leave.
– Keep all pages stapled together.
– Don’t use paper of your own; use the back of the sheets as scrap paper.
Cross out all scrap material after you have finished.
– Don’t use red ink (I grade using red ink).
– You can use pencil if you want.
– If your answer doesn’t fit in the allotted space, continue on the back and
clearly indicate so by writing Please turn over.
– Indicate in your answers where parts a, b, c, . . . start.
– Explain and show your work. Report which formulas you use.
– Use your scientific calculator and your laminated formula sheet.
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1. A histogram of monthly wages for part-time employees is shown below (densities are marked in parentheses). Nobody earned more than $ 1 000 a month.
The block over the class interval from $ 200 to $ 500 is missing. How tall must it
be? Explain and show your work. (Note that the horizontal units are hundreds
of dollars, not dollars.)
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2. The Public Health Service found that for boys age 11 in HANES2, the
average height was 146 cm and the SD was 8 cm. The histogram follows the
normal curve. Fill in the blanks. Show your work.
(a) One boy was 170 cm tall. He was above average, by
SDs.
(b) Another boy was 148 cm tall. He was above average, by
SDs.
(c) A third boy was 1.5 SDs below average height. He was
cm tall.
(d) If a boy was within 2.25 SDs of average height, the shortest he could have
been is
cm and the tallest is
cm.
(e) Here are the heights of four boys: 150 cm, 130 cm, 165 cm, 140 cm. Match
the heights with the descriptions. A description may be used twice, or not
at all. Briefly explain and show your work.
unusually short
about average
unusually tall
(f) About what percentage of boys of age 11 in the study had heights between
138 cm and 154 cm? Between 130 and 162 cm? (Answer without using
the calculator.)
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3. A longitudinal study of human growth was started in 1929 at the Berkeley
Institute of Human Development. The scatter diagram below shows the heights
of 64 boys, measured at ages 4 and 18.
(a) The average height at age 4 is around
38 inches 42 inches 44 inches
(b) The SD of height at age 18 is around
0.5 inches 1.0 inches 2.5 inches
(c) The correlation coefficient is around
0.50 0.80 0.95
Explain your answers.
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4. A deck of cards is shuffled, and two cards are dealt. What is the chance
that both cards are red cards? Explain which rules of chance you used and
show your work. (Note. A deck of cards has 52 cards. There are four suits:
Diamonds, Hearts, Clubs, and Spades. Diamonds and Hearts are red, Clubs
and Spades are black. Each suit contains 13 cards: 1 (Ace), 2, 3, 4, 5, 6, 7, 8,
9, 10, Jack, Queen, King. Dealing means drawing without replacement.)
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