HW 1 - Displaying Distributions with Graphs

Suppose the histogram shows the distribution of test scores for Ms. Bassoe's first grade class. Select the terms that describe the shape of the histogram.

-right (positively) skewed -an outlier present

Suppose that a random variable z has a standard normal distribution. Use a standard normal table such as this one to determine the probability that z is between -1 and 0.67. Give your answer in a decimal form, precise to at least three decimal places.

.590

Choose four numbers with the largest possible standard deviation. You may use the same number more than once. Is your selection of numbers the only possible correct answer?

1) First number: 0 Second number: 0 Third number: 5 Fourth number: 5 2) Yes

Suppose Ted is creating a football team in a video game that features many NFL players. He decides to identify players who are outliers in a few statistics he has chosen. Currently, he's looking at wide receivers. The game includes the top 100 receivers in 2012 by number of receptions. Ted, however, is more interested in receiving yards, and the table shows the five-number summary of the available players in the game (in yards): The mean is 787.6 yds with a standard deviation of 311.3 yds. Ted first calculates the interquartile range (IQR). Next, to determine suspected outliers, he calculates Q1−1.5⋅IQRQ1−1.5⋅IQR and Q3+1.5⋅IQRQ3+1.5⋅IQR. Specify those results to at least one decimal place. Ted identified the top five receivers available in the game by the number of receiving yards. Select the suspected outliers in receiving yards from the available receivers in the game.

1) Q1 − 1.5 ⋅ IQR = -31 Q3 - 1.5 ⋅ IQR = 1517 2) -Calvin Johnson -Andre Johnson

Suppose classmates who graduated in 2004 compared their median incomes ten years later. The bar graph displays the median income, in thousands of dollars, for each classmate during the time intervals from 2005-2009 and 2010-2014. For the individual with the largest dollar value increase in median income over the two time intervals, determine the amount of increase. By what percentage did Roger's median income decrease over the two time intervals? Give your answer to the nearest percent.

1) $11,000 2) 8%

Chronic wasting disease is a fatal disease of deer and elk believed to be caused by transmissible prions. The origin, development, and spread of chronic wasting disease in free-ranging deer and elk populations are not well understood. One factor directly related to the control of chronic wasting disease is the incubation period in free-ranging animals. Boxplots are shown for estimates of the incubation period of chronic wasting disease in North American deer and elk between 2011 and 2016. Select the year with a mean of 5050 months, a median of 6060months, and a small standard deviation for the incubation period of chronic wasting disease. Select the year with a mean of 5050 months, a median of 6060months, and a large standard deviation for the incubation period of chronic wasting disease.

1) 2013 2) 2016

Suppose that a polling company surveyed 600 people about how much time they spend reading each week. The results of this survey were compiled and used to create this relative frequency histogram. Assume that all percentages shown in the histogram are whole numbers. Each of the bars in this histogram includes only the left endpoint of the class except for the last bar, which also includes the right endpoint. What percentage of respondents said that they read less than 90 minutes per week? How many respondents said that they read between 60 and 120 minutes per week? Which of the following statements about the amount of time the respondents spend reading is true?

1) 70% 2) 198 respondents 3) Fewer than 10% of respondents spend at least 210 minutes reading each week

The Centers for Disease Control and Prevention (CDC) estimated the percent of individuals in each state who are classified as overweight or obese in different years. They calculated the estimates separately for three different age classes, including children (2-4 years old), adolescents (students in grades 9-12), and adults (aged 18 years and older). The boxplots display the given five‑number summaries (Min, First Quartile (Q1),Median, Third Quartile (Q3),MaxMin, First Quartile (Q1),Median, Third Quartile (Q3),Max) computed based on the data for two different age classes. Match the appropriate descriptions to the data sets.

1) Adults who were overweight -25% of values are less than 34.70 -the distribution is skewed to the right -25% of the values are more than 36.58 2)Children who were overweight -25% of values are less than 15.00 -the distribution is close to symmetrical -25% of the values are more than 16.75

Choose four numbers with the smallest possible standard deviation. You may use the same number more than once. Is your selection of numbers the only possible correct answer?

1) Fill in all numbers with the same number from answer bank (doesn't matter what number you pick) 2) No

Suppose that Jason recently landed job offers at two companies. Company A reports an average salary of $51,500 with a standard deviation of $2,150. Company B reports an average salary of $46,820 with a standard deviation of $5,890. Assume that salaries at each company are normally distributed. Jason's goal is to secure a position that pays $55,000 per year. What are the zz‑scores for Jason's desired salary at Company A and Company B? Please round your answers to two decimal places. At which company is Jason more likely to obtain his desired salary of $55,000 per year?

1)Company A z: 1.63 Company B z: 1.39 2)Company B, because the zz‑score for $55,000 at Company B is less than the zz‑score for $55,000 at Company A.

Classify each described variable as categorical or quantitative.

Categorical: -breed of a dog -rating of a hotel with the options of good, moderate, or bad -a person's country of origin Quantitative: -amount of rainfall -meal cost at a restaurant in dollars -temperature in degrees Celsius

Classify each of the narratives below based on whether the mean or median provides a better description of the center of its distribution.

Mean: -points scored by professional basketball players -hours of sleep per day for an American adult -caloric intake per day for an American adult Median: -age of professional basketball players -height of professional basketball players -commute time per day for an American adult

Arrange the histograms in ascending order of standard deviation.

Smallest - Largest -Age started smoking -Age of U.S. men with hypertension -Age of diabetes diagnosis -Age of U.S. men in the Northeast

The Bureau of Labor Statistics (BLS) collects data regarding occupational employment and wage estimates in the United States. The stem-and-leaf plot below represents the annual wage estimates, in thousands of dollars, for 15 select architecture and engineering occupations in May 2014. Identify all of the true statements regarding the given data.

The annual wage of $108,000 was the largest wage estimate for architecture and engineering occupations in May 2014. The modal class is 100 to 110 thousand dollars, with five occupations having salaries in that class.

The Centers for Medicare and Medicaid Services (CMS) use their databases containing medical claims data to summarize different health measures. Using data collected for the population of Medicare beneficiaries, the CMS create tables that summarize chronic disease prevalences. Disease prevalance is the percentage in a population that have a certain disease at a point in time. A portion of a table summarizing chronic disease prevalences by state for 2015 is given. This table portion includes prevalence data for a subset of the chronic diseases at the state level for several states.

The prevalence of arthritis in each state: variable The name of each state: label, variable In 2015, the prevalence of depression in Arizona was 12.9%: value The state of Georgia: case As of 2015, 7.7% of the Medicare beneficiary population in Hawaii had depression: value The prevalence of chronic kidney disease in each state: variable

Suppose that the weekly unit sales for two small franchise stores in Florida and Colorado are recorded over a one year period. The following boxplots display the resulting weekly unit sales in intervals of 25. Select all of the statements that describe the two boxplots above.

Weekly unit sales in Florida are more consistent than weekly sales in Colorado. The median of weekly unit sales in Florida is equivalent to the median of weekly sales in Colorado. Weekly unit sales in Colorado have more extreme values than weekly sales in Florida.

A random sample taken from a normally distributed population has the zz‑score of aa. Find aa such that P(z>a)=0.102P(z>a)=0.102 and specify your answer to two decimal places. You may find this zz‑table useful.

a = 1.27

Suppose a biologist is studying the population of fish in freshwater lakes. He collects data on the number of different species of fish found in 20 lakes. The boxplot displays the results of the study with species of fish in intervals of 50. Create a five-number summary of the data set. Round values to the nearest 25 species.

min = 75 species Q1 = 150 species median = 275 species Q3 = 350 species max = 550 species

Suppose students who enter kindergarten at Sotomayor Elementary School take a standardized vocabulary assessment. The scores on the vocabulary assessment produce a normal density curve as shown. From the graph shown, estimate the mean, median, and the standard deviation of the vocabulary assessment.

mean = 100 median = 100 standard deviation = 27

The ages in years of 21 people in a swimming pool are displayed in the stem-and-leaf plot. Determine the median age of people in the pool.

median = 16 years

Ortega-Jimenez et. al. recently concluded a study on the effects of water surface perturbations on the locomotion of Aquarius remigis, the common water strider. As part of their study, Ortega-Jimenez et. al. recorded the degree of 10 newborn water striders' pitch Ppitch P when striding. Suppose there is a well‑known linear relationship between a water strider's pitch as a newborn PnewbornPnewborn and its pitch as a juvenile Pjuvenile.pitch as a juvenile Pjuvenile. Use the data in the file to compute the sample mean, ¯¯¯xjuvenilex¯juvenile, and standard deviation, sjuvenilesjuvenile, of PjuvenilePjuvenile, the juvenile striders' pitch measurements while striding. Report your answers to two decimal places.

xjuvenile = 8.34 sjuvenile = 2.80