Question

 

Mean of stock price = 1117.64

STDEV (Population) = 67.61

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 (round to two places)? (Hint: this means the probability of being between 50 below and 50 above the mean).

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 $1050 per share (round to two places)? Would this be considered unusual? Use the definition that an unusual value is more than 2 standard deviations above or below the mean.

3. At what prices would Google have to close in order for it to be considered statistically unusual or statistically significant outliers? You will have a low and high value. There are several possible definitions for unusual in statistics, but for our project let's use the definition that an unusual value is more than 2 standard deviations above or below the mean.

Answer 1

u = 1117.64, = 67.61

z = (x-u)/

1) probability of being between 50 below and 50 above the mean

i.e. from (x-u) = -50 to (x-u) = 50

Thus, required probability

= (-50/67.61 < z < 50/67.61)

= P(z < 50/67.61) - P(z < -50/67.61)

= 0.7703 - 0.2297

= 0.5406

2) x = 1050

=> z = (1050 - 1117.64) / 67.61

z = -1.00

This is 1 standard deviation below mean. Thus, it is not unusual

3) for unusual values,

z < -2 or z > 2

Thus, (x-u)/ < -2 or (x-u)/ > 2

Thus, x < u - 2* or x > u + 2*

Thus, x < 1117.64 - 2*67.61 or x > 1117.64 + 2*67.61

Thus, x < 982.42 or x > 1252.86

Thus, anything outside of the range (982.42, 1252.86) will be considered as outlier