Section 3.2 HW

Find the population variance and standard deviation: 6, 15, 27, 33, 39 (Type an integer or a decimal. Round to one decimal place as​ needed.) A. s^2 = ___________ A.1 σ^2 = ________________ Choose the correct answer below. Fill in the answer box to complete your choice. ​(Round to one decimal place as​ needed.) B. σ = ___________ B.1 s = ____________

A. s^2 = ___________ A.1 σ^2 = 144 B. σ = 12 B.1 s = ____________

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 17. Use the empirical rule to determine the following. (Type an integer or a​ decimal.) ​(a) What percentage of people has an IQ score between 83 and 117​? ​(b) What percentage of people has an IQ score less than 49 or greater than 151​? ​(c) What percentage of people has an IQ score greater than 117​?

(a) 68 % (b) 0.3 % (c) 16 %

A certain standardized​ test math scores have a​ bell-shaped distribution with a mean of 520 and a standard deviation of 119. Complete parts​ (a) through​ (c). (Round to one decimal place as​ needed.) (a) What percentage of standardized test scores is between 163 and 877 ​? ​(b) What percentage of standardized test scores is less than 163 or greater than 877? ​(c) What percentage of standardized test scores is greater than 758?

(a) 99.7 % (b) 0.3 % (c) 2.5 %

Match the histograms on the right to the summary statistics given. Number Mean Median St.Dev I 57 57 1.9 II 66 66 9 III 57 57 10 IV 57 57 18 (a) (b) (c) (d)

(a) I (b) II (c) III (d) IV

The standard deviation is used in conjunction with the​ __(a)____ to numerically describe distributions that are bell shaped. The​ ___(b)___ measures the center of the​ distribution, while the standard deviation measures the​ ___(c)___ of the distribution.

(a) mean (b) mean (c) spread

Compute the range and sample standard deviation for strength of the concrete​ (in psi): 3940, 4120, 3100, 3200, 2960, 3860, 4120, 4030 (a) The range is _________ psi. (b) s = _______ psi​ (Round to one decimal place as​needed.)

(a) range: 1160 (b): sample st. dev. : 491.8

The following data represent the flight time​ (in minutes) of a random sample of seven flights from one city to another city. 282, 268, 258, 264, 255, 261, 267 Compute the range and sample standard deviation of flight time. (a) The range of flight time is __________ minutes. (b) The sample standard deviation of flight time is ___________ minutes. ​(Type an integer or decimal rounded to one decimal place as​ needed.)

(a) range: 27 (b) sample st. dev. : 8.8

Find the sample variance and standard deviation: 8, 49, 14, 51, 34, 28, 32, 32, 32, 31 ​(Round to two decimal places as​ needed.) A. sigma squared = _______________ s^2 = ___________ A.1 s squared = ______________ σ^2 = ________________ Choose the correct answer below. Fill in the answer box to complete your choice. ​(Round to one decimal place as​ needed.) B. s = ___________ B.1 σ = ____________

A. sigma squared = _______________ s^2 = 173.66 A.1 s squared = ______________ σ^2 = ________________ B. s = 13.2 B.1 σ = ____________

Find the sample variance and standard deviation: 20, 15, 4, 10, 8 ​(Type an integer or a decimal. Round to one decimal place as​ needed.) A. sigma squared = _______________ σ^2 = ___________ A.1 s squared = ______________ s^2 = ________________ Choose the correct answer below. Fill in the answer box to complete your choice. ​(Round to one decimal place as​ needed.) B. σ = ___________ B.1 s = ____________

A. sigma squared = _______________ σ^2 = ________ A.1 s squared = ______________ s^2 = 38.8 B. σ = _________ B.1 s = 6.2

Which histogram depicts a higher standard​ deviation? Histogram A: Freq. : 1, 2, 6, 7, 8, 9, 7, 7, 3, 1 Histogram B: Frequency: 2, 2, 2, 6, 9, 8, 5, 4, 3 A. Histogram b depicts the higher standard​ deviation, since it is more bell shaped. B. Histogram a depicts the higher standard​ deviation, because the bars are higher than the average bar in b. C. Histogram b depicts the higher standard​ deviation, because the distribution has more dispersion. D. Histogram a depicts the higher standard​ deviation, because the distribution has more dispersion.

C. Histogram b depicts the higher standard​ deviation, because the distribution has more dispersion.

The sum of the deviations about the mean always equals _____________________

Zero

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. A. ​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. B. ​False, because the standard deviation measures the spread of the​ distribution, not the dispersion of the distribution. C. ​True, because the standard deviation is the difference between the largest and smallest observation. When the standard deviation is​ larger, there is more distance between the largest and smallest​ observation, and​ therefore, more dispersion in the distribution. D. ​False, because the larger the standard deviation​ is, the less dispersion the distribution has.

​A. 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.