Warm-Up Grab a sheet of multiple choice questions and work on those!
Transcript of Warm-Up Grab a sheet of multiple choice questions and work on those!
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Warm-Up• Grab a sheet of multiple choice questions and work on those!
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Answers to warm-up (C C B D E)Homework Questions?
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Computer Outputs
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Finish Section 2.1
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Density Curves
1. Always plot your data: dotplot, stemplot, histogram…2. Look for overall pattern (SOCS)3. Calculate numerical summary to describeAdd a step…4. Sometimes the overall pattern is so regular we can describe
it by a smooth curve.
A Density Curve is a curve that:• Is always on or above the horizontal axis• Has an area of 1 underneath it
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Things to note…• The mean is the physical balance point of a density curve or a
histogram
• The median is where the areas on both sides of it are equal
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Don’t forget…• The mean and the median are equal for symmetric density
curves!
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Start Section 2.2Normal Curves!
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Normal Distributions = Normal Curves
• Any particular Normal distribution is completely specified by two numbers: its mean () and standard deviation ().
• We abbreviate the Normal distribution with mean and standard deviation as N()
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The 68-95-99.7 Rule
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Other images to explain the same thing…in case it helps!
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Example• A pair of running shoes lasts on average 450 miles, with a
standard deviation of 50 miles. Use the 68-95-99.7 rule to find the probability that a new pair of running shoes will have the following lifespans.
Between 400-500 miles
More than 550 miles
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Warm-Up (09-26-13)On the driving range, Tiger Woods practices his golf swing with a particular club by hitting many, many golf balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 288 yards?
What percent of Tiger’s drives travel between 296 and 320 yards?
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Example• The ACT and SAT are both Normally distributed with a mean of 18
and 1500 (respectively) and standard deviation of 6 and 300 (again respectively). Using this information find the following:
a. Percentage of scores that are above a 24 on the ACT.
b. Percentile for a 2100 on the SAT.
c. Percentage of ACT scores that are between 24 and 30.
d. Percentage of SAT scores that are between 900 and 1800.
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Example• A vegetable distributor knows that during the month of August, the
weights of its tomatoes were normally distributed with a mean of 0.61 pound and a standard deviation of 0.15 pound.
a. What percent of the tomatoes weighed less than 0.76 pound?
b. In a shipment of 6000 tomatoes, how many tomatoes can be expected to weigh more than 0.31 pound?
c. In a shipment of 4500 tomatoes, how many tomatoes can be expected to weigh between 0.31 and 0.91 pound?
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How does this relate to z-scores?
• If the distribution happens to be normal we can find the area under the curve and percentiles by using z-scores!
• Standard Normal distribution – mean of 0 and standard deviation of 1.
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Table A in your book…• The table entry for each z-score is the area under the curve to
the left of z.
• If we wanted the area to the right, we would have to subtract from 1 or 100%
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Examples• Find the proportion of observations that are less than 0.81
• Find the proportion of observations that are greater than -1.78
• Find the proportion of observations that are less than 2.005
• Find the proportion of observations that are greater than 1.53
• Find the proportion of observations that are between -1.25 and 0.81
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Homework• Page 107: 19-38 (Density Curves)• Page 131: 41-54 (Normal Curves and z-scores)