1 Kingdom of Saudi Arabia
Ministry of Education Umm AlQura University
Adam University College, female branch Computer Science Department
ةيدوعسلا ةيبرعلا ةكلمملا ميلعتلا ةرازو ةعماج ىرقلا مأ تابلاطلا رطش ،مضأب ةيعماجلا ةيلكلا
يللآا بساحلا مولع مسق
First Semester of 2017-2018 Academic Year
Elementary Statistics, 6803131-3 Revision Excercises
Question One:
Check the following data set for outliers:
14, 16, 27, 18, 13, 19, 36, 15, 20.
The Answer of Question One
1.Arrange the Data From Lowest to Highest:
13, 14, 15, 16, 18, 19, 20, 27, 36.
2.Find Q1 and Q3:
Q2 = median = 18 Q1 = 15
Q3 = 20
3.Find the Interquartile(IQR = Q3-Q1):
IQR: Q3-Q1 = 20-15 = 5.
4.Multiply the Interquartile by 1.5:
5*1.5 = 7.5
5.Subtract the value from Q1 and add the value to Q3, we get:
15 – 7.5 = 7.5.
20 + 7.5 = 27.5
6.Check the data set for any value that is outside the interval (7.5, 27.5):
36 is outside the interval!
So it’s considered to be an outlier.
Question Two:
Working Women and Computer Use It is reported that 72% of working women use computers at work.
Choose 5 working women at random. Find
a. The probability that at least 1 doesn’t use a computer at work b. The probabilty that all 5 use a computer in their jobs
Source: www.infoplease.com
The Answer of Question Two
a.
(𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) = (𝟎. 𝟕𝟐)𝟓= 𝟎. 𝟏𝟗𝟑𝟒𝟗𝟏𝟕𝟔𝟑𝟐 𝐏(𝐀𝐭 𝐥𝐞𝐚𝐬𝐭 𝟏 𝐝𝐨𝐞𝐬𝐧’𝐭 𝐮𝐬𝐞 𝐚 𝐜𝐨𝐦𝐩𝐮𝐭𝐞𝐫 𝐚𝐭 𝐰𝐨𝐫𝐤) = 𝟏 − 𝟎. 𝟏𝟗𝟑 = 𝟎. 𝟖𝟎𝟕
b. 𝐏(𝐀𝐥𝐥 𝟓 𝐮𝐬𝐞 𝐚 𝐜𝐨𝐦𝐩𝐮𝐭𝐞𝐫) = (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) ∗ (𝟎. 𝟕𝟐) = (𝟎. 𝟕𝟐)𝟓= 𝟎. 𝟏𝟗𝟑𝟒𝟗𝟏𝟕𝟔𝟑𝟐
2 Question Three:
High School Dropouts Approximately 10.3% of American high school students drop out of school before graduation. Choose 10 students entering high school at random. Find the probability that
a. No more than two drop out b. At least 6 graduate
c. All 10 stay in school and graduate
Source: www.infoplease.com
You can use the formula or Table B.
The Answer of Question Three
n = 10, p = 0.103, q = 0.897.
𝐏(𝑿) = 𝒏!
(𝒏 − 𝑿)! 𝑿!(𝒑)𝑿(𝒒)𝒏−𝑿 Fom Table:
a.𝐏(𝐍𝐨 𝐦𝐨𝐫𝐞 𝐭𝐡𝐚𝐧 𝐭𝐰𝐨 𝐝𝐫𝐨𝐩 𝐨𝐮𝐭) = 𝐏(𝟎) + 𝐏(𝟏) + 𝐏(𝟐) = 𝟎. 𝟑𝟒𝟗 + 𝟎. 𝟑𝟖𝟕 + 𝟎. 𝟏𝟗𝟒 = 𝟎. 𝟗𝟑
b.𝐏(𝐀𝐭 𝐥𝐞𝐚𝐬𝐭 𝟔 𝐠𝐫𝐚𝐝𝐮𝐚𝐭𝐞) = 𝐏(𝟔) + 𝐏(𝟕) + 𝐏(𝟖) + 𝐏(𝟗) + 𝐏(𝟏𝟎) = 𝟎. 𝟎𝟖𝟖 + 𝟎. 𝟐𝟎𝟏 + 𝟎. 𝟑𝟎𝟐 + 𝟎. 𝟐𝟔𝟖 + 𝟎. 𝟏𝟎𝟕 = 𝟎. 𝟗𝟔𝟔
Using Formula:
b. 𝐏(𝐀𝐥𝐥 𝐠𝐫𝐚𝐝𝐮𝐚𝐭𝐞) = 𝐏(𝟔) = 𝟏𝟎!
(𝟏𝟎−𝟏𝟎)!𝟏𝟎!(𝟎. 𝟖𝟗𝟕)𝟏𝟎(𝟎. 𝟏𝟎𝟑)𝟏𝟎−𝟏𝟎= 𝟎. 𝟑𝟑𝟕𝟐𝟐𝟖𝟔𝟐𝟒
Question Four:
Find the area under the standard normal distribution curve to the left of z= -0.75.
The Answer of Question Four:
1.Draw the Curve:
2.From Table E:
The Area is 0.2266
3 Question Five:
Distribution of Population in U.S. Cities A random sample of U.S. cities is selected to determine if there is a relationship between the population (in thousands) of people under 5 years of age and the
population (in thousands) of those 65 years of age and older.
The data for the sample are shown here.
Under 5 x 178 27 878 314 322 143
65 and over y 361 72 1496 501 585 207
Source: New York Times Almanac.
a.Compute the value of the correlation coefficient, is there a relationship?
b.Draw the scatter plot.
The Answer of Question Five:
a.
Under 5 x 65 and over y XY X2 Y2
178 361 64258 31684 130321
27 72 1944 729 5184
878 1496 1313488 770884 2238016
314 501 157314 98596 251001
322 585 188370 103684 342225
143 207 29601 20449 42849
Sum = 1862 Sum = 3222 Sum = 1754975 Sum = 1026026 Sum = 3009596
𝒓 = 𝒏(𝚺𝒙𝒚) − (𝚺𝒙)(𝚺𝒚)
√[𝒏(𝚺𝒙𝟐) − (𝚺𝒙)𝟐][𝒏(𝚺𝒚𝟐) − (𝚺𝒚)𝟐]
𝟔(1754975 ) − (1862)(3222)
√[𝟔(1026026) − (1862)𝟐][𝟔(3009596) − (3222)𝟐] = 𝟎. 𝟗𝟗𝟕𝟏𝟓𝟗𝟒𝟑𝟕𝟕
The value is near to 1, then there’s a strong positive linear ralationship between the two variables.
b.
Good Luck my Great Students 😉 T. Mariah Sami Ahmed Khayat
Teacher Assistant @ Adam University College [email protected]
0 200 400 600 800 1000 1200 1400 1600
0 200 400 600 800 1000
65 and Over
Under 5
