QUIZ 6

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers. 57 49 43 47 32 31 30 40 67 39

-What is the​ mean? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A. The mean is 43.543.5. ​(Round to one decimal place as​ needed.) -What is the​ median? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A. The median is 41.541.5.​ (Round to one decimal place as​ needed.) -What​ is(are) the​ mode(s)? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. B. There is no mode.

After recording the pizza delivery times for two different pizza​ shops, you conclude that one pizza shop has a mean delivery time of 44 minutes with a standard deviation of 4 minutes. The other shop has a mean delivery time of 43 minutes with a standard deviation of 22 minutes. Interpret these figures. If you liked the pizzas from both shops equally​ well, which one would you order​ from? Why?

-The means are nearly​ equal, but the variation is significantly greater for the second shop than for the first. -Choose the first shop. The delivery time is more reliable because it has a lower standard deviation.

Briefly describe the use of the range rule of thumb for interpreting the standard deviation. What are its​ limitations?

-The standard deviation is approximately the range divided by four. The range rule of thumb does not work well when the highest or lowest value is an outlier.

Consider the distribution of exam scores​ (graded from 0 to​ 100) for 86 students when 38 students got an​ A, 28 students got a​ B, and 20 students got a C. Complete parts​ (a) through​ (d) below.

-There would probably be one peak because there are no obvious reasons why the exam scores would form different groups. -A Smallest line -The distribution would probably be​ left-skewed because many of the students got an​ A, and very few got a C. -The variation would probably be large because many students got an​ A, some got a​ B, and a small number got a​ C, and so the data are not clustered.

Describe the process of calculating a standard deviation. Give a simple example of its calculation​ (such as calculating the standard deviation of the numbers​ 2, 3,​ 4, 4, and​ 6). What is the standard deviation if all of the sample values are the​ same?

-subtracting the mean from -squares -add -total number of data values minus 1. -square root -1.483 -0

What is a normal​ distribution? Briefly describe the conditions that make a normal distribution.

A normal distribution is a​ symmetric, bell-shaped distribution with a single peak. Its peak corresponds to the​ mean, median, and mode of the distribution. Its variation is characterized by the standard deviation of the distribution.

Exam results for 100 students are given below. For the given exam​ grades, briefly describe the shape and variation of the distribution. median=68​, mean=70​, low score=65​, high score=

Right skewed low

The number of times that people change jobs during their careers.

The median because it is unaffected by outliers.

I examined the data​ carefully, and the range was greater than the standard deviation.

The statement makes sense because the range is approximately four times the standard deviation.

An acquaintance tells you that his IQ is in the 102nd percentile. What can you conclude from this​ information?

You can conclude that he​ doesn't understand percentiles because it is impossible to be in the 102nd percentile.

The highest exam score was in the upper quartile of the distribution.

The statement makes sense because the highest score will be in the highest quartile.

Exam results for 100 students are given below. For the given exam​ grades, briefly describe the shape and variation of the distribution. median=79​, mean=73​, low score=6​, high score=81

left-skewed high

State, with an​ explanation, whether you would expect the following data sets to be normally distributed. The last digit of the Social Security number of 1000 randomly selected people.

The data set is not expected to be normally distributed. Of the people randomly​ selected, there could be more digits greater than 5 or more less than​ 5, which would skew the distribution.

Find the mean and median for the waiting times at Best Bank given below. Show your work​ clearly, and verify that both are the same. The following values are measured in minutes. Best Bank​ (one line): 6.6 6.7 6.7 6.9 7.1 7.2 7.3 7.4 7.7 7.8 7.8

The median is the 6th value in the sorted data set. -7.2 -equal to

Define and distinguish among​ mean, median, and mode.

-The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers. -The median is the middle value in a data set. It is not affected by outliers. -The mode is the most common value in a data set. It is not affected by outliers.

Suppose a car driven under specific conditions gets a mean gas mileage of 40 miles per gallon with a standard deviation of 3 miles per gallon. On about what percentage of the trips will your gas mileage be above 43 miles per​ gallon?

About​ 16%, because 43 miles per gallon is 1 std. deviation above the mean. By the​ 68-95-99.7 rule, about​ 68% of the distribution lies within 1 std. deviation of the mean. So​ 32% lies outside of this​ range, 16% in each tail.

Scores on the quantitative section of a certain graduate school entrance exam are normally distributed with a mean of 146 and a standard deviation of 9.1. Scores for a certain group of students range between 132 and 173. What are the percentiles of these​ scores?

The percentile of the score 132 is 6.206.20​%. Part 2 The percentile of the score 173 is 99.8599.85​%.

Scores on the quantitative section of a certain graduate school entrance exam are normally distributed with a mean of 155 and a standard deviation of 9.2. Scores for a certain group of students range between 139 and 178. What are the percentiles of these​ scores?

The percentile of the score 139 is 4.10​%. Part 2 The percentile of the score 178 is 99.38​%

What is the​ 68-95-99.7 rule for normal​ distributions? Explain how it can be used to answer questions about frequencies of data values in a normal distribution.

The rule states that about​ 68%, 95%, and​ 99.7% of the data points in a normal distribution lie within​ 1, 2, and 3 standard deviations of the​ mean, respectively.

For the 30 students who took the​ test, the high score was​ 80, the median was​ 75, and the low score was 40.

The statement makes sense because it is possible that when sorting the 30 scores from low to​ high, the first value was​ 40, the highest value was​ 80, and 75 was halfway between the 15th and the 16th score.

In a normal​ distribution, where do about 2/3 of the data values​ fall?

They fall within 1 standard deviation of the mean. This is because by the​ 68-95-99.7 rule, approximately​ 68% or​ two-thirds of all data points in a normal distribution fall within 1 standard deviation of the mean.

Suppose you read that the average height of a class of 36 ​eighth-graders is 49 inches with a standard deviation of 39 inches. Is this​ likely? Explain.

This is not likely because a mean of 49 and a standard deviation of 39 would imply that about​ 5% of the heights differ from the mean by more than 78​, which is impossible

My professor graded the final score on a​ curve, and she gave a grade of A to anyone who had a standard score of 2 or more.

This makes sense because a standard score of 2 or more corresponds to roughly the 97th percentile. Though this curve is stingy on giving out​ A's to​ students, it is still giving the top students the highest grade.

Decide whether the following statement makes sense or does not make sense. Explain your reasoning. Jack is in the 50th percentile for​ height, so he is of median height.

This makes sense. The 50th percentile height means that​ 50% of all the heights in the data set are less than or equal to​ Jack's height. The median is the middle​ value, which means it splits the distribution in half. These two statements are the same.

Consider the following set of three​ distributions, all of which are drawn to the same scale. Identify the two distributions that are normal. Of the two normal​ distributions, which one has the larger​ variation?

a and b b -b has the smallest curve c's curve starts quickly

Consider the following set of three​ distributions, all of which are drawn to the same scale. Identify the two distributions that are normal. Of the two normal​ distributions, which one has the larger​ variation?

a and c c

Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 5. Use the​ 68-95-99.7 rule to find the following quantities.

a. The percentage of scores less than 80 is 50.0​%. Part 2 b. The percentage of scores greater than 85 is 16.0​%. Part 3 c. The percentage of scores between 70 and 85 is 81.5​%.