Mathematics
MM 305 PGU Business Statistics and Quantitative Analysis

MM 305

Purdue Global University

MM

Question Description

I’m trying to learn for my Statistics class and I’m stuck. Can you help?

Read a classmate’s response. Consider investing in your classmate’s stock and assume that the daily change is normally distributed. Using the Normal Distribution Excel template found in Unit 4 LiveBinder, your classmate’s mean and standard deviation, determine the probability for the daily change of this stock to have:
1. A decrease of 0.5 point or more (X ≤ -0.5)?
2. An increase of more than 0.5 point (X > 0.5)?
3. A decrease of 1 point or more (X ≤ -1)?
4. An increase of more than 1 point (X > 1)

Adjust automatic marking as read setting
  1. I chose the stock for Xcel Energy, Inc.
  2. The daily change of this stock is:

Date

Open

High

Low

Close

Adj Close

Volume

Daily Change

2/7/2020

69.49

69.54

68.7

68.71

68.26784

2316900

-0.78

2/10/2020

68.91

69.12

68.54

69.06

68.61559

2306300

0.149994

2/11/2020

69.06

69.23

68.84

68.96

68.51623

2176200

-0.1

2/12/2020

68.75

69.25

68.55

69.03

68.58578

2032500

0.279999

2/13/2020

69.08

69.89

68.92

69.82

69.37069

2430700

0.739998

2/14/2020

69.99

70.4

69.77

70.26

69.80786

1959400

0.270004

2/18/2020

70.63

71.43

70.57

71.16

70.70207

3552200

0.530007

2/19/2020

70.94

71.24

70.77

70.79

70.33445

2284500

-0.15

2/20/2020

70.74

70.99

70.19

70.67

70.21523

2243900

-0.07

2/21/2020

70.72

71.42

70.44

70.82

70.36426

3563600

0.099999

2/24/2020

71.69

72.14

70.22

70.37

69.91716

3531000

-1.32

2/25/2020

70.48

70.65

68.73

68.84

68.397

3581800

-1.64001

2/26/2020

69.32

69.49

68.32

68.35

67.91015

3060200

-0.97

2/27/2020

68.33

68.67

64.81

64.85

64.43268

4225400

-3.48

2/28/2020

64.08

64.08

61.25

62.32

61.91896

7762100

-1.76

3/2/2020

62.22

65.99

62.15

65.87

65.44611

5117800

3.650002

3/3/2020

65.42

67.46

65.2

65.71

65.28714

5425200

0.290001

3/4/2020

66.53

69.41

66.06

69.2

68.75468

3454200

2.669998

3/5/2020

67.84

70.02

67.45

69.25

68.80436

5871800

1.410004

3/6/2020

66.51

70.16

66.23

70.15

69.69857

6689400

3.64

3/9/2020

66.36

69.99

65.3

67.99

67.55247

9885200

1.629997

3/10/2020

68.55

70.68

66.1

68.49

68.04925

8897400

-0.06001

3/11/2020

67.03

68.23

65.63

66.82

66.39

5815100

-0.21

3/12/2020

63.06

66.98

59.57

61.29

61.29

7310900

-1.77

3/13/2020

63.37

66.85

61

66.84

66.84

5724700

3.469997

3/16/2020

60.86

67

57.41

58.36

58.36

7884300

-2.5

3/17/2020

59.74

67.26

59.64

64.93

64.93

8959300

5.189998

3/18/2020

61.49

64

57.67

61.37

61.37

6690300

-0.12

3/19/2020

61.53

62.48

57.24

57.99

57.99

6840300

-3.54

3/20/2020

59

59.15

50.03

50.63

50.63

9147400

-8.37

  1. The descriptive statistics summary table:

Daily Change

Mean

-0.0940006

Standard Error

0.469059349

Median

-0.0650025

Mode

#N/A

Standard Deviation

2.569143864

Sample Variance

6.600500194

Kurtosis

2.919792966

Skewness

-0.759032478

Range

13.559997

Minimum

-8.369999

Maximum

5.189998

Sum

-2.820018

Count

30

  1. Here is my 5-Number Summary:

Five Number Summary

Minimum

-8.37

First quartile

-1.2325

Median

-0.065

Third quartile

0.6875

Maximum

5.189998

  1. The Box & Whiskers Plot does not look very symmetric
  1. The Mean, Xbar= -0.094 < Median -0.065

From this information and also the box plot, you can tell my daily stock price is not symmetric but instead slightly left-skewed.


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Final Answer

Attached.

Probability
1
2
3
4

Expression
X ≤ -0.5
X > 0.5
X ≤ -1
X>1

obability
Probability
0.42
0.42
0.35
0.35

1.

2.

4.

3.

z-score associated with the confidence interval left side
Lower x value for the confidence level
Upper x value for the confidence level

> can be replace with >= , and < can be replaced by x)

Probability value is outside a range of values for x
Upper x
lower x
P(value is > ...

UT Austin

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