What is variation why is it IMPORTANT Wachovia

What is variation & why is it IMPORTANT? Wachovia Bank (single waiting line) 4 minutes 7 minutes BB&T Bank (multiple waiting lines) 1 minute 3 minutes 14 minutes a. ) find the mean for both sets of data. b. ) find the median for both sets of data. c. ) find the range for both sets of data. d. ) find the standard deviation for both sets of data. Based on the different variations calculated in a-d, what would you advise the banks to do to improve customer satisfaction: use single waiting line or multiple waiting lines?

about 68% of a data set lies in the range about 95% of a data set lies in the range almost all of a data set lies in the range 34% of your data 13. 5% of your data 2. 35% of your data 0. 15% of your data Normal Distribution

Standard normal distribution

In the Tree Tops The heights (in feet) of fully grown white oak trees are normally distributed with a mean of 90 feet and a standard deviation of 3. 5 feet. 1) About what percent of white oak trees have heights between 86. 5 feet and 93. 5 feet? 2) In a forest of 123 white oak trees, about how many trees have heights between 86. 5 feet and 93. 5 feet? 3) Find the probability that a randomly selected white oak tree has a height of at most 94 feet. 4) Find the probability that a randomly selected white oak tree has a height of at most 13 feet.

POPULATION VS SAMPLE

POPULATION VS SAMPLE POPULATION – includes all objects of interest that have common characteristics • Parameter - characteristic or measure obtained from a population – usually denoted using letters (N, m, σ) SAMPLE – a subgroup or subset of the population, used represents the population. • Statistic - characteristic or measure obtained from a sample – are usually denoted using letters (n, x, s)

POPULATION VS SAMPLE WHY IS THERE A NEED FOR SAMPLING? • Populations are usually large • It is often impossible to get data for every object we're studying. • Sampling does not usually occur without cost, and the more items surveyed, the larger the cost. • Time of research or collection of data.

Population vs. Sample Population: the complete collection of all elements. The collection is complete in the sense that it includes all subjects to be studied Sample: a sub collection of members selected from a population Population Mean Standard Deviation Z-scores Sample of a population

Stanford Binet IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160. a. ) What is the difference between Einstein’s IQ and the mean? b. ) How many standard deviations is that (the difference found in part a. )? c. ) If we consider “usual” IQ scores to be those that are ± 2 standard deviations from the mean, is Einstein’s IQ usual or unusual? d. ) Convert Einstein’s IQ score to a z-score. e. ) If we consider “usual” IQ scores to be those that convert to zscores between -2 and 2, is Einstein’s IQ usual or unusual?

HW • Pg. 221 #12 -18

Assume that adults have a pulse rates (beats per minute) with a mean of 72. 9 and a standard deviation of 12. 3. a. ) Calculate one member’s pulse rate (count the pulse for 6 seconds then multiple by 10). b. ) What is the difference between your group member’s pulse rate and the mean? c. ) How many standard deviations is that from the mean? Is this usual or unusual? d. ) Convert the pulse rate to a z-score. e. ) If we consider “usual” pulse rates to be those that convert to zscores between -2 and 2, is your group member’s pulse rate usual or unusual? f. ) Can you explain why a pulse rate would be unusually high or low?

Adult males have heights with a mean of 69. 0 inches and a standard deviation of 2. 8 inches. Find the z-scores to the following and determine is the heights are “usual. ” a. ) Actor Danny Devito, who is 5 feet tall b. ) NBA basketball player Shaquille O’Neal, who is 7 ft 1 in. tall c. ) Choose a male member of your group to measure and compare using a z-score.

The Beanstalk Club is limited to men and women who are very tall. The minimum height requirement for women is 70 inches. Women’s heights have a mean of 63. 6 inches and a standard deviation of 2. 5 inches. a. ) Find the z-score corresponding to a woman with a height of 70 inches and determine whether the height is unusual. b. ) Julia Roberts has a height that converts to a z-score of 2. 2. How tall in inches is Julia Roberts? And in feet? c. ) Lil’ Kim has a height that converts to a z-score of -1. 84. How tall in inches is Lil’ Kim? And in feet? d. ) Select a female from your group and calculate her height z-score. Is your group member’s height “usual? ”

a. ) Which is relatively better: a score of 85 on a math test or a score of 45 on a physics test? Scores on the math test have a mean of 90 and a standard deviation of 10. Scores on the physics test have a mean of 55 and a standard deviation of 5. b. ) Three students take equivalent tests of a sense of humor and, after the laughter dies down, their scores are calculated. Which is the highest relative score: 1. ) A score of 144 on a test with a mean of 128 and a standard deviation of 34. 2. ) A score of 90 on a test with a mean of 86 and a standard deviation of 18. 3. ) A score of 18 on a test with a mean of 15 and a standard deviation of 5.

Convert the weight of the heaviest green M&M candy to a z -score. Is the weight of the heaviest green M&M an unusual weight for green M&M’s? Weight in grams of a SAMPLE of green M&M’s: 0. 911 1. 002 0. 930 0. 949 0. 890 0. 902 Complete all calculations by hand.

At the Super Bowl of 2008, the New York Giants beat the New England Patriots 17 to 14. Convert the Giants’ points to it’s corresponding z-score. Was this an unusual winning score? Why or why not? Winning Super Bowl points from 1980 -2000 (is this a population or a sample? ): 50, 37, 57, 44, 47, 54, 56, 59, 36, 65, 39, 61, 69, 43, 75, 44, 56, 55, 53, 39, 41 Complete all calculations by hand.

a. ) Find 5 number summaries, construct box-plots, and make generalized comparisons between the POPULATION data sets: Age of Actor when Awarded an Oscar: 32 37 36 32 51 53 33 61 35 45 55 39 76 37 42 40 32 60 38 56 48 48 40 43 62 43 42 44 41 56 39 46 31 47 45 60 46 40 36 Age of Actress when awarded an Oscar: 50 44 35 80 26 28 41 21 61 38 49 33 74 30 33 41 31 35 41 42 37 26 34 34 35 26 61 60 34 24 30 37 31 27 39 34 26 25 33 b. ) The Oscar went to Daniel Day-Lewis in 2008 for Best Actor. His age at the time was 51. Convert his age to a z-score. Is this a usual outcome? c. ) The Oscar went to Marion Cotillard in 2008 for Best Actress. Her age at the time was 33. Convert her age to a z-score. Is this a usual outcome? d. ) Ellen Page, star of Juno, was also nominated for best actress at age 20. Why do you think she didn’t win. Use probability to back your claim.