{"id":97907,"date":"2022-10-03T14:57:21","date_gmt":"2022-10-03T14:57:21","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/3-points-on-an-exam-with-a-mean-of-m-82-you-obtain-a-score-of-x\/"},"modified":"2022-10-03T14:57:21","modified_gmt":"2022-10-03T14:57:21","slug":"3-points-on-an-exam-with-a-mean-of-m-82-you-obtain-a-score-of-x","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/3-points-on-an-exam-with-a-mean-of-m-82-you-obtain-a-score-of-x\/","title":{"rendered":"(3 points) on an exam with a mean of m = 82, you obtain a score of x"},"content":{"rendered":"
\n

\u00a0<\/p>\n

1.\u00a0\u00a0\u00a0 (3 points) On an exam with a mean of\u00a0<\/span><\/strong><\/span>M<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 82, you obtain a score of\u00a0<\/span><\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/em><\/strong><\/span>=86.<\/span><\/strong><\/p>\n

a.\u00a0\u00a0\u00a0 Would you prefer a standard deviation of\u00a0<\/span><\/span><\/strong>s<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 2 or\u00a0<\/span><\/span><\/strong>s<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 10? (<\/span><\/strong>Hint<\/span><\/strong><\/em>: Sketch each distribution and find the location of your score.)<\/span><\/strong><\/p>\n

b.\u00a0\u00a0\u00a0 If your score were\u00a0<\/span><\/span><\/strong>X = 78,<\/span><\/strong><\/em>\u00a0<\/span><\/em><\/strong><\/span>would you prefer\u00a0<\/span><\/span><\/strong>s<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 2 or\u00a0<\/span><\/span><\/strong>s = 10?\u00a0<\/span><\/strong><\/em>Explain your answer.<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

2.\u00a0 (3 points) \u00a0\u00a0A student was asked to compute the mean and standard deviation for the following sample of\u00a0<\/span><\/strong><\/span>n<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 5 scores: 81, 87, 89, 86, and 87.\u00a0 To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7.\u00a0 The mean and standard deviation for the new sample were then calculated to be\u00a0<\/span><\/span><\/strong>M<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 6 and\u00a0<\/span><\/span><\/strong>x<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 3.\u00a0 What are the values of the mean and standard deviation for the original sample?<\/span><\/strong><\/p>\n

3.\u00a0 (3 points) \u00a0\u00a0<\/span><\/p>\n

Calculate\u00a0<\/span><\/span><\/strong>SS<\/span><\/strong><\/em>, variance, and standard deviation for the following population of\u00a0<\/span><\/span><\/strong>N<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 7 scores: 8, 1, 4, 3, 5, 3, 4.\u00a0(<\/span><\/strong>Note:<\/span><\/strong><\/em>\u00a0<\/span><\/em><\/strong><\/span>The definitional formula works well with these scores.)<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

4.\u00a0 (3 points) For the following population of\u00a0<\/span><\/strong><\/span>N<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 6 scores: 5, 0, 9, 3, 8, 5<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

a.\u00a0\u00a0\u00a0 Sketch a histogram showing the population distribution.<\/span><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

a.\u00a0\u00a0\u00a0 <\/span><\/span><\/span><\/strong>Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example, 4.2).<\/span><\/strong><\/p>\n

\u00a0<\/span><\/strong><\/p>\n

b.\u00a0\u00a0\u00a0 <\/span><\/span><\/span><\/strong>Compute\u00a0<\/span><\/span><\/strong>SS<\/span><\/strong><\/em>, variance, and standard deviation for the population.\u00a0 (How well does your estimate compare with the actual value of \u03c3?)<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

5.\u00a0 (3 points) A distribution has a standard deviation of \u03c3 = 12.\u00a0 Find the\u00a0<\/span><\/span><\/strong>z<\/span><\/strong><\/em>-score for each of the following locations in the distribution.<\/span><\/strong><\/p>\n

a.\u00a0\u00a0\u00a0 Above the mean by 3 points.\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

b.\u00a0\u00a0\u00a0 Above the mean by 12 points.\u00a0\u00a0 <\/span><\/span><\/p>\n

c.\u00a0\u00a0\u00a0 Below the mean by 24 points.\u00a0\u00a0 <\/span><\/span><\/p>\n

d.\u00a0\u00a0\u00a0 Below the mean by 18 points.\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

6.\u00a0 (5 points) For a population with a mean of \u00b5 = 100 and a standard deviation of 12<\/span><\/strong><\/p>\n

a.\u00a0\u00a0\u00a0 Find the\u00a0<\/span><\/span><\/strong>z<\/span><\/strong><\/em>-score for each of the following\u00a0<\/span><\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>values.<\/span><\/strong><\/p>\n

X<\/span><\/em>\u00a0<\/span><\/em><\/span>= 106\u00a0\u00a0\u00a0 <\/span><\/span>X<\/span><\/em>\u00a0<\/span><\/em><\/span>= 115\u00a0\u00a0\u00a0 <\/span><\/span>X<\/span><\/em>\u00a0<\/span><\/em><\/span>= 130\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

X<\/span><\/em>\u00a0<\/span><\/em><\/span>= 91\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

X<\/span><\/em>\u00a0<\/span><\/em><\/span>= 88\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

X<\/span><\/em>\u00a0<\/span><\/em><\/span>= 64\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

b.\u00a0\u00a0\u00a0 Find the score (<\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>value) that corresponds to each of the following <\/span><\/strong>z<\/span><\/strong><\/em>-scores.<\/span><\/strong><\/p>\n

z<\/span><\/em>\u00a0<\/span><\/span>= – 1.00\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

z<\/span><\/em>\u00a0<\/span><\/span>= – 0.50\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

z<\/span><\/em>\u00a0<\/span><\/span>= 2.00\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span>z<\/span><\/em>\u00a0<\/span><\/span>= 0.75\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

z<\/span><\/em>\u00a0<\/span><\/span>= 1.50\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

z<\/span><\/em>\u00a0<\/span><\/span>= – 1.25\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

7.\u00a0 (3 points) Find the\u00a0<\/span><\/span><\/strong>z<\/span><\/strong><\/em>-score corresponding to a score of\u00a0<\/span><\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 60 for each of the following distributions.<\/span><\/strong><\/p>\n

a. \u00b5 = 50 and \u03c3 = 20\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

b. \u00b5 = 50 and \u03c3 = 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

c. \u00b5 = 50 and \u03c3 = 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span><\/span><\/p>\n

d. \u00b5 = 50 and \u03c3 = 2\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

8.\u00a0 (1 point) A score that is 6 points below the mean corresponds to a <\/span><\/strong>z<\/span><\/strong><\/em>-score of\u00a0<\/span><\/span><\/strong>z<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= – 0.50.\u00a0 What is the population standard deviation?<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

9.\u00a0 (3 points) For each of the following, identify the exam score that should lead to the better grade.\u00a0 In each case, explain your answer.<\/span><\/strong><\/p>\n

a.\u00a0\u00a0\u00a0 A score of\u00a0<\/span><\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/em><\/strong><\/span>= 56, on an exam with \u00b5 = 50 and \u03c3 = 4, or a score of <\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 60 on an exam with \u00b5 = 50 and \u03c3 = 20.<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

b.\u00a0\u00a0\u00a0 <\/span><\/span><\/span><\/strong>A score of\u00a0<\/span><\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/em><\/strong><\/span>= 40, on an exam with \u00b5 = 45 and \u03c3 = 2, or a score of <\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 60 on an exam with \u00b5 = 70 and \u03c3 = 20.<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

c.\u00a0\u00a0\u00a0 A score of\u00a0<\/span><\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/em><\/strong><\/span>= 62, on an exam with \u00b5 = 50 and \u03c3 = 8, or a score of <\/span><\/strong>X<\/span><\/strong><\/em>\u00a0<\/span><\/strong><\/span>= 23 on an an exam with \u00b5 = 20 and \u03c3 = 2.<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

1. \u00a0For the following set of scores, find the value of each expression.\u00a0 (5 points)<\/span><\/strong><\/p>\n

X<\/span><\/span><\/em><\/strong>
-4
-2
0
-1
-1<\/span><\/strong><\/p>\n

\u00a0<\/span><\/p>\n

2.\u00a0 Construct a frequency distribution table for= the following set of scores.\u00a0 Include columns for proportion and percentage in your table. (5 points)<\/span><\/strong><\/p>\n

Scores: 5, 7, 8, 4, 7, 9, 6, 6, 5, 3, 9, 6, 4, 7, 7, 8, 6, 7, 8, 5<\/span><\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0<\/span><\/p>\n

3.\u00a0 The following scores are the ages for a random sample of\u00a0n<\/em>\u00a0= 30 drivers who were issued speeding tickets in New York during 2008.\u00a0 Determine the best interval width and place the scores in a grouped frequency distribution table.\u00a0 From looking at your= table, does in appear the tickets are issued equally across age groups? (5= points)<\/span><\/strong><\/p>\n

17,\u00a0 30,\u00a0 45,\u00a0 20,\u00a0 39,\u00a0 53,28,\u00a0 19<\/span><\/p>\n

24,\u00a0 21,\u00a0 34,\u00a0 38,\u00a0 22,\u00a0 29, 64<\/span><\/p>\n

22,\u00a0 44,\u00a0 36,\u00a0 16,\u00a0 56,\u00a0 20, 23,\u00a0 58<\/span><\/p>\n

32,\u00a0 25,\u00a0 28,\u00a0 22,\u00a0 51,\u00a0 26, 43<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n
\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0<\/span><\/p>\n

No the tickets are not distributed equally among all age groups.<\/span><\/p>\n

\u00a0<\/span><\/p>\n

4.\u00a0 Find the mean, median, and mode for the scores in the following frequency distribution table. (5 points)<\/span><\/strong><\/p>\n

_____<\/span><\/strong><\/p>\n

\u00a0 X\u00a0<\/span><\/span><\/em><\/strong>\u00a0\u00a0\u00a0 <\/span>\u00a0\u00a0f\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>f*X\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>cf <\/em><\/span><\/span><\/strong><\/p>\n

\u00a0<\/span><\/strong><\/p>\n

10\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>10\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>15<\/span><\/strong><\/p>\n

\u00a0 9\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>18\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>14<\/span><\/strong><\/p>\n

\u00a0 8\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>24\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>12<\/span><\/strong><\/p>\n

\u00a0 7\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>21\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>9<\/span><\/strong><\/p>\n

\u00a0 6\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>24\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>6<\/span><\/strong><\/p>\n

\u00a0 5\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>10\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>2<\/span><\/strong><\/p>\n

\u00a0<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u00a0 1.\u00a0\u00a0\u00a0 (3 points) On an exam with a mean of\u00a0M\u00a0= 82, you obtain a score of\u00a0X\u00a0=86. a.\u00a0\u00a0\u00a0 Would you prefer a standard deviation of\u00a0s\u00a0= 2 or\u00a0s\u00a0= 10? (Hint: Sketch each distribution and find the location of your score.) b.\u00a0\u00a0\u00a0 If your score were\u00a0X = 78,\u00a0would you prefer\u00a0s\u00a0= 2 or\u00a0s = 10?\u00a0Explain your answer. \u00a0 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-97907","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/97907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=97907"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/97907\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=97907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=97907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=97907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}