Sta - Chapter 3; Part 1 (3.1-3.3)
A sample of college students was asked how much they spent monthly on pizza. Approximate the mean for the cost.
$36.97. Takes a lot of work, work this problem via StatCrunch.
The weight of an organ in adult males has a bell-shaped distribution with a mean of 340 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following. (a) About 95% of organs will be between what weights? (b) What percentage of organs weighs between 280 grams and 400 grams? (c) What percentage of organs weighs less than 280 grams or more than 400 grams? (d) What percentage of organs weighs between 300 grams and 400 grams?
(a) 300 and 380 grams (b) 99.7% (c) 0.3% (d) 97.35%
A doctor randomly selects 40 of his patients and obtains the following frequency distribution diagram regarding their serum HDL cholesterol. Use the frequency distribution diagram on the right to approximate the mean and standard deviation for serum HDL. (a) x (overbar) = (b) s = (c) Using the actual data, the sample mean, x (overbar), is found to be 46.3 and the sample standard deviation, s, is 11.9. Compare the approximate mean to the actual mean. (d) Compare the approximate sample standard deviation to the actual sample standard deviation.
(a) 46.25 (b) 11.6 (c) The approximate x (overbar) is slightly smaller than the actual x (overbar). (d) The approximate s is slightly smaller than the actual s.
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 78 and 122? (b) What percentage of people has an IQ score less than 67 or greater than 133? (c) What percentage of people has an IQ score greater than 111?
(a) 95% (b) 0.3% (c) 16%
A random sample of 15 college students were asked "How many hours per week typically do you work outside the home?" Their responses are shown on the right. Determine the shape of the distribution of hours worked by drawing a frequency histogram and computing the mean and median. Which measure of central tendency better describes hours worked? Table shown. (a) Choose the correct frequency histogram below. (b) Is the histogram for the data set skewed right, skewed left, or symmetric? (c) What is the mean number of hours? (d) What is the median number of hours? (e) Which measure of central tendency better describes hours worked?
(a) Graphic shown. (Skewed right) (b) Skewed right (c) 12.933 hours (d) 13 hours (e) median
An insurance company crashed four cars of the same model at 5 miles per hour. The costs of repair for each of the four crashes were $434, $401, $482, and $227 . Compute the mean, median, and mode cost of repair. (a) Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (b) Compute the median cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (c) Compute the mode cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(a) The mean cost of repair is $386. (b) The median cost of repair is $417.5. (c) The mode does not exist.
The following data represent the pulse rates (beats per minute) of nine students enrolled in a statistics course. Treat the nine students as a population. Complete parts (a) to (c). Table shown. (a) Determine the population mean pulse. (b) Determine the sample mean pulse of the following two simple random samples of size 3. Sample 1: {Janette, Clarice, Kathy} Sample 2: {Perpectual, Clarice, Janette} (c) Determine if the means of samples 1 and 2 overestimate, underestimate, or are equal to the population mean.
(a) The population mean pulse is approximately 72.3 per minute. (b) The mean pulse of sample 1 is approximately 67.3 per minute. The mean pulse of sample 2, is approximately 69.3 per minute. (c) The mean pulse rate of sample 1 underestimates the population mean. The mean pulse rate of sample 2 underestimates the population mean.
The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the range and sample standard deviation for ATM fees for each city. Which city has the most dispersion based on range? Which city has more dispersion based on the standard deviation? Graphic shown. (a) What is the range for city B?? (b) What is the standard deviation for city A? (c) What is the standard deviation for city B? (d) Which city has the most dispersion based on range? (e) Which city has the most dispersion based on standard deviation?
(a) The range for city B is $0.50. (b) The standard deviation for city A is $0.89. (c) The standard deviation for city B is $0.27. (d) City A, because it has a higher range. (e) City A, because it has a higher standard deviation.
The data set below on the left represents the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the data set below on the right represents the annual rate of return (in percent) of eight randomly sampled stock mutual funds. Use the information in the table below to complete parts (a) through (d). Then complete part (e). Table shown. (a) Determine the mean and standard deviation of each data set. i. What is the mean of the data set for bond mutual funds? ii. What is the standard deviation of the data set for bond mutual funds? iii. What is the mean of the data set for stock mutual funds? iv. What is the standard deviation of the data set for stock mutual funds? (b) Based only on the standard deviation, ______ have more spread. (c) What proportion of the bond mutual funds are within one standard deviation of the mean? i. What proportion of the stock mutual funds are within one standard deviation of the mean? (d) The coefficient of variation, CV, is defined as the ratio of the standard deviation to the mean of a data set. The CV allows for a comparison in spread by describing the amount of spread per unit mean. Compute the CV for both data sets. i. What is the CV of the data set for bond mutual funds? ii. What is the CV of the data set for stock mutual funds? iii. Based on the coefficient of variation, ______ have more spread. (e) In the table below, the data set on the left has the heights of students measured in inches, while the data set on the right has the same students' heights measured in centimeters. For each data set, determine the mean and the standard deviation. Draw a conclusion about the spread using the standard deviation, then find the coefficient of variation for both data sets. i. What is the mean of the data set for height in inches? ii. What is the standard deviation of the data set for height in inches? iii. What is the mean of the data set for height in centimeters? iv. What is the standard deviation of the data set for height in centimeters? v. Based on the standard deviation, the data set for height in ______ has more spread. vi. What is the CV of the data set for height in inches? vii. What is the CV of the data set for height in centimeters? viii. What is true of the coefficient of variation?
(a) i. 2.275 ii. 0.669 iii. 7.913 iv. 0.903 (b) stock mutual bonds (c) 0.625 i. 0.625 (d) i. 0.294 ii. 0.114 iii. bond mutual funds (e) i. 30.375 ii. 3.543 iii. 178.753 iv. 8.999 v. centimeters vi. 0.050 vii. 0.050 vii. When converting units of measure, the coefficient of variation is unchanged.
A sample of college students was asked how much they spent monthly on pizza. Approximate the standard deviation for the cost.
?
Clarissa has just completed her second semester in college. She earned a grade of C in her 5-hour discrete math course, a grade of C in her 2-hour sociology course, a grade of A in her 3-hour engineering course, and a grade of A in her 3-hour studio art course. Assuming that A equals 4 points, B equals 3 points, C equals 2 points, D equals 1 point, and F is worth no points, determine Clarissa's grade-point average for the semester.
Clarissa's GPA is 2.92.
The standard deviation can be negative.
False
True or False: A data set will always have exactly one mode.
False
For the histogram on the right determine whether the mean is greater than, less than, or approximately equal to the median. Justify your answer.
Graphic shown. x (overbar) < M because the histogram is skewed left.
The U.S. Department of Housing and Urban Development (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the median?
HUD uses the median because the data are skewed right.
Which histogram depicts a higher standard deviation? Graphic shown.
Histogram b depicts the higher standard deviation, because the distribution has more dispersion.
Suppose the first class in a frequency table of quantitative data is 0-4 and the second class is 5-9. What is the class midpoint of the first class?
The class midpoint is 2.5.
Stan and Francine want to make perfume. In order to get the right balance of ingredients for their tastes they bought 5 ounces of rose oil at $3.82 per ounce, 2 ounces of ginger essence for $4.08 per ounce, and 5 ounces of black currant essence for $2.09 per ounce. Determine the cost per ounce of the perfume.
The cost of the perfume is $3.14.
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
The mean square footage is 2444 (overbar) = ?
A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be larger, the mean or the median? Why?
The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.
The median for the given set of six ordered data values is 29.5. 9 12 25 __ 41 49 What is the missing value?
The missing value is 34.
Find the population variance and standard deviation. 3, 6, 10, 12, 14
The population variance is 16. The standard deviation is 4.
The following data represent the flight time (in minutes) of a random sample of seven flights from one city to another city. 287, 270, 260, 266, 257, 264, 258 Compute the range and sample standard deviation of flight time.
The range of flight time is 30 minutes. The sample standard deviation of flight time is 10.3 minutes.
Find the population mean or sample mean as indicated. Sample: 19, 10, 1, 9, 16,
The sample mean is 11.
The standard deviation is used in conjunction with the ______ to numerically describe distributions that are bell shaped. The ______ measures the center of the distribution, while the standard deviation measures the ______ of the distribution.
mean, mean, spread
The histogram on the right represents the connection time in seconds to an internet provider. Determine which measure of central tendency better describes the "center" of the distribution. What measure of central tendency best describes the "center" of the distribution? Graphic shown.
median
Find the sample variance and standard deviation. 22, 13, 6, 10, 12
s^2=34.8 s=5.9
The sum of the deviations about the mean always equals ______
zero
The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
μ = 45.66, σ = 10.79. Takes a lot of work, work this problem via StatCrunch.
True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.
True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
