Question

The data table is too large to be put in the question here is where I collected the data:

Visit the NASDAQ historical prices weblink(https://finance.yahoo.com/quote/GOOG/history/). First, set the date range to be for

1.16.18- 2.15.19. [Do this by clicking on the blue dates after “Time Period”. Next, click the “Apply” button. Next, click the link on the right side of the page that says “Download Data” to save the file to your computer].

Normal distribution Average=1110.68525 Standard Deviation= 65.5518337 Mode= 1095.06006

1. 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? (between 50 below and 50 above the mean)c) 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?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 $950?

2. 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 $800 per share. Would this be considered unusal?
3. At what prices would Google have to close in order for it to be considered statistically unusual?
4. 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. Is the normality assumption that was made at the beginning valid? Why or why not?

Answer 1

Sol:

Downloaded data for the time period range1.16.18- 2.15.19

using descriptive statistics in excel for the column close

Mean	1110.685251
Standard Error	3.9601311
Median	1099.264954
Mode	1095.060059
Standard Deviation	65.5518337
Sample Variance	4297.042902
Kurtosis	-0.744581395
Skewness	0.351349751
Range	292.109985
Minimum	976.219971
Maximum	1268.329956
Sum	304327.7587
Count	274

mean=1110.685251

sample sd=65.5518337

n=274

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? (between 50 below and 50 above the mean

mean-50=1060.685

mean+50=1160.685

P(1060.685<xbar<1160.685)

=P(1060.685-1110.685251/65.5518337<1160.685-1110.685251/65.5518337)

=P(-0.762759<Z<0.7627514)

simply by entering the below one line of command in R studio we get the area between limits

pnormGC(bound=c(1060.685,1160.685),region="between", mean=1110.685251,sd=65.5518337,graph=TRUE)

=0.5543906

Solutionb:

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 $950?

P(X>950)

pnormGC(bound=950,region="above", mean=1110.685251,sd=65.5518337,graph=TRUE)

=0.9928823

2. 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 $800 per share. Would this be considered unusal?

P(X<800)

pnormGC(bound=800,region="below", mean=1110.685251,sd=65.5518337,graph=TRUE)

1.071043e-06

ANSWER:0.0000

since probability less than 0.05

it is considered unusual.

What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values.

QUARTILE(E2:E275;1) QUARTILE(E2:E275;2) QUARTILE(E2:E275;3)
that is Q1 1060.395 Q2 1099.265 Q3 1163.827

2. Is the normality assumption that was made at the beginning valid? Why or why not?

here sample szie=n=274

large sample

n>30

follows normal distribution according to central limit theorem