# 1. Mean of the closing stocks= 625.31

Statistics 4

1.Mean of the closing stocks= 625.31

Probabilityfor less than mean= Probability for X< 625.31 = Probability of Z<(625.31-625.31/Standard deviation) = Probability (Z< 0 )= 0.5.

Thisis because for a standard normal distribution, the area less than 0is 0.5. The probability of Z< 0 gives the area under the standardnormal distribution less than zero, which is equal to 0.5.

Hence,if a person bought 1 share of Google stock within the last year, whatis the probability that the stock on that day closed at less than themean for that year is 0.5 .

2.Mean of the closing stocks= 625.31. Standard deviation of closingstocks=19.89.

Probabilityof X>$600 = Probability of Z >( (600-625.31)/19.89)=Probability of Z> -1.272

=0.602.

Thisis the area under the standard normal distribution greater than-1.272.

Thus,if a person bought one share of Google stock within the last year,what is theprobabilitythat the stock on that day closed at more than $600 is 0.602.

3.Meanof the closing stocks= 625.31. Standard deviation of closingstocks=19.89.

Probabilityof 45<X< 625.31= Probability of 45< X + Probability of X<625.31 =Probability of Z< ( 45-625.31)/19.89 + Probability of Z<0 = Probability of Z< -29.176 +0.5= 0.00003 +0.5= 0.50003.

Ifa person bought 1 share of Google stock within the last year, theprobabilitythat the stock on that day closed within $45 of the mean for thatyear = 0.50003.

4. Meanof the closing stocks= 625.31. Standard deviation of closingstocks=19.89.

Probabilityof X<=450= Probability of Z= ( 450- 625.31/ 19.89) = Probabilityof Z= -8.814 = 0.

Theprice is considered unusual since the probability of the point at-8.814 is zero, which means the area under the standard normaldistribution in this case is zero. Thus, a person within the last year claimed to have bought Google stock atclosing at $450 per share is said to be having unusual price.

5. Meanof high prices= 634.04

Meanof low prices= 617.76

Standarddeviation of high prices= 16.75

Standarddeviation of low prices= 21.04

Forthe prices to be considered unusual, they need to be outside therange of high prices [Mean +- 2* Standard deviation] = [600.55 ,667.53] and also outside the range of low prices [Mean +- 2*Standard deviation] = [575.69, 659.89]. The unusual prices will beoutside the range ofthese high and low prices.

Ifwe consider the close prices only, the unusual prices lie within therange of [ 625.31+- 2* 19.89 ]= [585.42, 665.09].

Anyprices which Google close lying outside the range of these high andlow prices are considered as statistically unusual prices.

6. Table1 shows the first, second and third quartile values for the close and volume values based on the Larson and Farber website given.

Table 1: Quartile Values for theClosing Prices and Volume

Quartiles |
Close |
Volume |

Quartile 1 |
613.125 |
1716596 |

Quartile 2 |
624.505 |
2154054 |

Quartile 3 |
635.845 |
2785379 |

7. Histogramis a method used to examine the appropriateness of normalityassumption. The following figure shows the histogram of the closingvalues by Google.

Itshows that it has the right shape of normal distribution. Hence, thenormality assumption made in the beginning is valid. This means thatall the calculations based on the normality assumption are logical.