Question

a) What the mean and Standard Deviation (SD) of the Close column in your data set?

b) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution. (5 points)

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $825? (5 points)

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year? (5 points)

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $700 per share. (5 points)

At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations. (5 points)

What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values. This is the only question that you must answer without using anything about the normal distribution. (5 points)

Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in the course textbook? Real data sets are never perfect, however, it should be close. One option would be to construct a histogram like you did in Project 1 to see if it has the right shape. Something in the range of 10 to 12 classes is a good number. (5 points)

List of Closed Stocks:

898.700012
911.710022
906.690002
918.590027
928.799988
930.090027
943.830017
947.159973
955.98999
953.419983
965.400024
970.890015
968.150024
972.919983
980.340027
950.700012
947.799988
934.090027
941.530029
930.5
930.830017
930.390015
923.650024
927.960022
929.359985
926.789978
922.900024
907.23999
914.390015
922.669983
922.219971
926.960022
910.97998
910.669983
906.659973
924.690002
927
921.280029
915.890015
913.809998
921.289978
929.570007
939.330017
937.340027
928.450012
927.809998
935.950012
926.5
929.080017
932.070007
935.090027
925.109985
920.289978
915
921.809998
931.580017
932.450012
928.530029
920.969971
924.859985
944.48999
949.5
959.109985
953.27002
957.789978
951.679993
969.960022
978.890015
977
972.599976
989.25
987.830017
989.679993
992
992.179993
992.809998
984.450012
988.200012
968.450012
970.539978
973.330017
972.559998
1019.27002
1017.109985
1016.640015
1025.5
1025.579956
1032.47998
1025.900024
1033.329956
1039.849976
1031.26001
1028.069946
1025.75
1026
1020.909973
1032.5
1019.090027
1018.380005
1034.48999
1035.959961
1040.609985
1054.209961
1047.410034
1021.659973
1021.409973
1010.169983
998.679993
1005.150024
1018.380005
1030.930054
1037.050049
1041.099976
1040.47998
1040.609985
1049.150024
1064.189941
1077.140015
1070.680054
1064.949951
1063.630005
1060.119995
1056.73999
1049.369995
1048.140015
1046.400024
1065
1082.47998
1086.400024
1102.22998
1106.939941
1106.26001
1102.609985
1105.52002
1122.26001
1121.76001
1131.97998
1129.790039
1137.51001
1155.810059
1169.969971
1164.23999
1170.369995
1175.839966
1175.579956
1163.689941
1169.939941
1167.699951
1111.900024
1055.800049
1080.599976
1048.579956
1001.52002
1037.780029
1051.939941
1052.099976
1069.699951
1089.52002
1094.800049
1102.459961
1111.339966
1106.630005
1126.790039
1143.75
1118.290039
1104.72998
1069.52002
1078.920044
1090.930054
1095.060059
1109.640015
1126
1160.040039
1164.5
1138.170044
1149.48999
1149.579956
1135.72998
1099.819946
1097.709961
1090.880005
1049.079956
1021.570007
1053.209961
1005.099976
1004.559998
1031.790039
1006.469971
1013.409973
1025.140015
1027.810059
1007.039978
1015.450012
1031.640015
1019.969971
1032.51001
1029.27002
1037.97998
1074.160034
1072.079956
1087.699951
1072.959961
1067.449951
1019.97998
1021.179993
1040.040039
1030.050049
1017.330017
1037.310059
1024.380005
1023.719971
1048.209961
1054.790039
1053.910034
1082.76001
1097.569946
1098.26001
1100.199951
1079.22998
1081.77002
1078.589966
1066.359985
1079.579956
1069.72998
1079.689941
1079.23999
1075.660034
1060.319946
1067.800049
1084.98999
1119.5
1139.290039
1139.660034
1136.880005
1123.859985
1120.869995
1129.98999
1139.319946
1134.790039
1152.119995
1152.26001
1173.459961
1168.060059
1169.839966
1157.660034
1155.47998
1124.810059
1118.459961
1103.97998
1114.219971
1115.650024

Answer 1

Let's find summary of the given data set using excel:

a) What the mean and Standard Deviation (SD) of the Close column in your data set?

From the above output sample mean = = 1033.17

and sample standard deviation = s = 76.56

b) If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution.

Under the normality assumption about half of the data less than the mean and half of the data are greater than the mean because of symmetry of normal distribution.

Therefore answer of this question is 0.5

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at more than $825

We want to find P( X > 825 ) = 1 - P(X < 825 ) ......( 1 )

Let's use excel:

P(X < 825 ) = "=NORMDIST(825, 1033.17,76.56,1)" = 0.0033

Plug this value in equation ( 1 ), we get

P( X > 825 ) = 1 - 0.0033 = 0.9967

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $50 of the mean for that year

That is we want to find P( - 50 < X < + 50 ) = P( 1033.17 - 50 < X < 1033.17 + 50)

= P( 983.17 < X < 1083.17) = P( X < 1083.17 ) - P( X < 983.17) ------( 2 )

P( X < 1083.17 ) = "=NORMDIST(1083.17,1033.17,76.56,1)" = 0.7431

P( X < 983.17 ) = "=NORMDIST(983.17,1033.17,76.56,1)" = 0.2569

Plug these values in equation 2), we get :

P( 983.17 < X < 1083.17) =  0.7431 -  0.2569 = 0.4862

If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than $700 per share.

Here we want to find P( X < 700)

P( X < 700) = "=NORMDIST(700, 1033.17,76.56,1)" = 0.0000068

Which is almost equal to zero.

At what prices would Google have to close in order for it to be considered statistically unusual? You will have a low and high value. Use the definition of unusual from the course textbook that is measured as a number of standard deviations.

the values which are lies outside the interval of two time standard deviation from the mean are the unusual observations

Lower limit = mean - 2 * standard deviation = 1033.17 - ( 2 * 76.56 ) = 880.05

Upper limit = mean + 2 * standard deviation = 1033.17 + ( 2 * 76.56 ) = 1186.29

Therefore the observations outside the ( 880.05, 1186.29) this interval are called unusual observation.