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Unformatted text preview: 9/21/2010 hw.sampDist.doc] HW.sampDist.&KEY Page 1 SAMPLING DISTRIBUTION HW Revised 09/21/10 FOR ALL HOMEWORK. [1] IF MORE THAN ONE PAGE, THEY MUST BE STAPLED.
OTHERWISE, NO CREDIT.
[2] NO RIPPEDOUT EDGES OF PAPER – ALL EDGES MUST
BE SMOOTH FOR CREDIT.
[3] SHOW ALL WORK, INCLUDING FORMULAS WITHOUT NUMBERS, USING SYMBOLS.
[4] TURN IN **BEFORE YOU SIT DOWN** EVEN IF I’M LECTURING. OTHERWISE NO
CREDIT. [5] UPPER RIGHT CORNER MUST HAVE YOUR CLASS ID.
Suppose the tire life is distributed as X ~ N(20,16) in 1000's of miles, and we intend to take a sample of 25.
The warranty mileage is 19,000 miles. (Saying this is in 1000’s of miles means that we can do
computations with a number like 19 instead of using 19,000.
#1. Compute P(if test one tire, this one tire will last longer than 19) and 19 means 19,000 miles. That is,
what is the probability that the particular tire we select will last beyond the warranty period? (Draw
the graph with 2 axes and fill in all pertinent information, and show with an arrow the area you are
looking for.)
a.
State the question as a probability: P(____________)
b.
Compute the probability; draw the normal graph with both axes and label everything
everything and show with an arrow the area you are looking for, as you’ll need to do for an
exam.
#2. Compute P(if we test a random group of 25, their average is more than 19). Draw the graph with
both axes.
a.
State the question as a probability: P(____________)
b.
Compute the probability; draw the normal graph with both axes and label everything and show
with an arrow the area you are looking for, as you’ll need to do for an exam. _ #3. How would one in theory for the tire mileage problem construct the sampling distribution of X? NEW EXAMPLE: A company claims its steel bars tend to be about 10 feet long. In fact, the length of the
2
individual bars is X ~ N(10,2 ). When they ship the bars, they ship either single bars, or groups of 49
bars.
#4. The foreman selected and shipped one bar out of the group. No one thought to measure the bar
before it was shipped, so the inventory control person needs to estimate its length. Compute the
probability that its length was more than 10.5 ft.
a.
State the question as a probability: P(____________)
b.
Compute the probability; draw the normal graph with both axes and label everything and show
with an arrow the area you are looking for, as you’ll need to do for an exam. 9/21/2010 HW.sampDist.&KEY Page 2 #5. What is along the top axis? (Each graph has 2 horizontal axes; the bottom one, and one on top of
that.) #6. What is along the bottom axis? #7. The foreman selects and ships one group of 49 bars. Compute the probability that the average length
of the group of 49 bars is less than 9.5 ft. Use both axes and label them.
a.
State the question as a probability: P(____________)
b.
Compute the probability; draw the normal graph with both axes and label everything and show
with an arrow the area you are looking for, as you’ll need to do for an exam. #8. What is along the top axis? (Each graph has 2 horizontal axes; the bottom one, and one on top of
that.) #9. What is along the bottom axis? end ...
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This note was uploaded on 01/19/2012 for the course GEOL 123 taught by Professor Kim during the Winter '11 term at Bowling Green.
 Winter '11
 kim

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