Part B.We tend to prize intelligence very highly, especially the kind of logical reasoning ability that is used a lot in QM1 and that can be measured using IQ tests. IQ tests are designed so that scores across the general public are normally distributed with mean 100 and standard deviation 15.(If you feel like trying a simple informal IQ test, just Google "online IQ test" and take your pick!)Suppose you score 115 on an IQ test. Where does that place your intelligence relative to the general public? Specifically:(a) what proportion of the population would be below 115?(b) what proportion of the population would be above 115?The ultimate in IQ is MarvinLinks to an external site. , who has "a brain the size of a planet". His IQ is astronomical, but for our purposes let's say it is 146. Where is Marvin's IQ placed relative to the general population.(Clearly Marvin is not very happy. In fact he spends a lot of time feeling very depressed. His astronomical IQ is not enough to make him happy.)Research has suggested that IQ alone may not be sufficient for a happy successful life. Angela Duckworth has led research suggesting that "grit" may be as important as IQ! Grit is "perseverance and passion in the pursuit of long term goals" and, as part of the research, a "grit scale" was developed.(You can meet Angela Duckworth hereLinks to an external site.... about 6 minutes, not necessary for the tutorial, but you may find it interesting. You can estimate your own grit hereLinks to an external site..)Grit scores are continuous between 0 and 5, with higher scores indicating greater grittiness. The percentiles of the distribution in the general population are given in the following table.Percentile Male Female10 2.51 2.5120 2.83 2.8830 3.06 3.1340 3.25 3.2550 3.38 3.5060 3.54 3.6370 3.75 3.7980 3.92 4.0090 4.21 4.25100 5.00 5.00(a) What are the median grit scores for males and females?(b) If Marvin is the ultimate in IQ, then the ultimate in grit is RickLinks to an external site.... he is never going to give you up! Rick scored 4.21 on the grit scale. Where does this place his grittiness relative to the general population?

1. (b) What proportion of the population would have IQ above 115? (express as a decimal, to 3 decimal places)

IQ scores are normally distributed with mean 100 and standard deviation 15.1. (b) What proportion of the population would have IQ above 115? (express as a decimal, to 3 decimal places)

The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, what range of IQ scores do many (68%) people have? Between 85 and 115 Between 70 and 130 Between 55 and 145 Less than 85 or more than 115 Above 100Question 2Select one answer.10 pointsThe distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, only 0.15% of people have an IQ over what score? 55 100 115 130 145Question 3Select one answer.10 pointsThe histogram below shows the times, in minutes, required for 25 rats in an animal behavior experiment to successfully navigate a maze.Which of the following are the appropriate numerical measures to describe the center and spread of the above distribution? The IQR and the standard deviation The median and the IQR The mean and the median The mean and the standard deviationQuestion 4Select one answer.10 pointsA student survey was conducted at a major university, and data were collected from a random sample of 750 undergraduate students. One variable that was recorded for each student was the student's answer to the question: “What region of the country did you live in just prior to enrolling in this university? Northeast/Southeast/Northwest/Southwest/Midwest/Outside the U.S.”These data would be best displayed using which of the following? IQR Histogram Pie chart Boxplot StemplotQuestion 5Select one answer.10 pointsThe boxplots below show the real estate values of single-family homes in two neighboring cities (in thousands of dollars).Which city has more households? Statstown Medianville Both cities have the same number of households. It is impossible to tell from the boxplots.Question 6Select one answer.10 pointsThe boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes.Which class has greater variability in students’ estimate of the number of marshmallows? Ms. Apple’s class Ms. Banana’s class Both classes have the same variability in students’ estimates. It is impossible to tell from the boxplots.Question 7Select one answer.10 pointsThe boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes.Which class has the greater percentage of estimates over 100? Ms. Apple’s class Ms. Banana’s class Both classes have the same percentage of estimates over 100. It is impossible to tell from the boxplots.Question 8Select one answer.10 pointsThe boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes.Which class has a greater percentage of estimates between 50 and 100 marshmallows? Ms. Apple’s class Ms. Banana’s class Both classes have the same percentage of estimates between 50 and 100. It is impossible to tell from the boxplots.Question 9Select one answer.10 pointsBased on the results of a nation-wide study, the number of contacts programmed into cell phones are summarized on the following boxplot:Which of the following is true about this data? The lowest observation is an outlier. The highest observation is an outlier. The data is skewed left. The data is skewed right. There are no outliers.Question 10Select one answer.10 pointsBased on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot:Which interval contains the greatest amount of data? 0–50 50–100 100–150 150–200 It is impossible to tell.

Which of the following is not true of the term IQ?Question 5Select one:a.Intelligence test scores of today are always based on the old formula of comparing a child’s mental age to their chronological ageb.Intelligence test scores of today are determined by comparing a person’s performance on the test with the performance of others in the same age groupc.Scores near 100 are average

The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county’s residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area.A researcher is hired to conduct a study to determine whether Smart County’s residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105.After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average, the p-value of 0.0004 was obtained.Using a 0.05 significance level, what conclusion can be drawn from the data? Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average. Do not reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average. Reject the null hypothesis. The average Full Scale IQ of Smart County residents is not higher than the population average. Reject the null hypothesis. The average Full Scale IQ of Smart County residents is higher than the population average.