Reviewquestions:1)What is meant, if data follow a bell curve or normal distribution?What are some examples of quantities that are typically normallydistributed?

Normaldistribution refers to probability distribution that represents aproportioned fashion of values and most placed around probability’smean. We say data is normally distributed if mean, median and mode isequal. Examples of quantities that are normally distributed includeheight, weight, and strength in general population and error ofmeasurement.2)What proportion of the data in a normal distribution lies within onestandard deviation of the mean? Within two standard deviations?Three?

Theproportion of data that lies within one, two and three standarddeviation is 68%, 95% and 99% respectively.Computationalexercises:1)Automated machinery is used to fill boxes of Chocolate Frosted SugarBombs breakfast cereal. The machine is calibrated to put an averageof 16.4 ounces of cereal in each box. Minor variation in the processcauses the standard deviation to be 0.2 ounces.a) Whatpercentage of the boxes of cereal weigh less than 16 ounces?

Z=Valuesubtracted by the mean divided by standard deviation.

=16 – 16.4 divided by 0.2

=-0.4/0.2

=-2

Probabilityassociated with 2 = 0.9772

=1 – 0.9772

=0.0228b) what percentage weigh between 16.2 and 16.8ounces?Answer:

Z= Value subtract by the Mean divided by the Standard Deviation

=16.2-16.4/0.2

=1

Probabilityassociated to 1 = 0.8413

=0.5 – 0.8413

=0.3413

=16.8 – 16.4/0.2

=2

Probabilityassociated to 2 = 0.9772

=0.5 – 0.9772

=0.4772

=0.3413 + 0.4772

=0.8185

c)What percentage are more than 17.4 ounces?Answer:

2= Value subtracted by the mean divided by the standard deviation

=17.4 – 16.4/0.2

=5

Probabilityassociated to 5 = 0.99997

=1 – 0.99997

=0.00001

Approximately= 0

2)A recent anthropological study of the aboriginal dwarf pygmies livingon the island of Kafoonistan has shown that adult males in the tribehave an average height of 60&quot, with a standard deviation of4&quot.a) What percentage of the men of the tribe areover six feet (72&quot) tall?Answer:

Z=value subtract by the mean divided by the standard deviation

2=72-60/4

=12/4

=3

Probabilityassociated to 3 = 0.99865

=0.5-0.99865

=0.0013

b)How tall are the tallest 10% of the men in the tribe?Answer:

Z= value subtract by the mean divide by the standard deviation

Z= X – 60/4

Zis constant associated to probability of 0.9 = 1.29

X– 60/4 = 1.29

X– 60 = 1.29 * 4

X= 60 + 5.16

X= 65.16c) How short are the shortest 20% of the men in thetribe?Answer:

Z= Value subtract by the mean divide by the standard deviation

Zis constant associated to probability of 0.8, which is 0.85

0.85= X – 60/4

X- 60 = 0.85 * 4

X– 60 = -3.4

X= -3.4 + 60

X= 56.6

3)Daily stock market returns on the Boravian Stock Exchange areapproximately normally distributed, with a mean of 0.05% and astandard deviation of 0.5%.

a)What percentage of the time are daily returns positive (i.e., greaterthan 0%)?Answer:

Mean= 0.05

StandardDeviation = 0.5

Value= 0

Z= Value subtract by the mean divide by the standard Deviation

Z= 0 – 0.05/0.5

Z= 0.1

Probabilityassociated to 0.1

=0.53983

b)What percentage of the time do daily returns drop by 2% or more?

Mean= 0.05

StandardDeviation = 0.5

Value= 2

Z= Value subtract by the mean divide by the standard Deviation

Z= 2 – 0.05/0.5 = 3.9

Probabilityassociated to 3.9

=0.99995

=1 – 0.99995

=0.00005

Approximately0

References

John,J. A., Whitaker, D., &amp Johnson, D. G. (2001).&nbspStatisticalthinking for managers.CRC Press.