3 A stock market analyst has kept records for the past sever

3. A stock market analyst has kept records for the past several years ofthe daily selling of a particular blue-chip stock. The resulting distribution of scores is normally distributed with a a standard of S6.94. a. Determine the percentage of selling prices that were below a price of $95.00. hat percentage of selling prices was between $76.00 and $88.00? b. c. What percentage of selling prices was above $70.00? would you make money if you d. You bought 10 shares at a price of $78.50. How often randomly picked a day to sell your shares? the mean and 25% e. What is the range of the average 50 of daily prices (i.e., 25% above below the mean)?

Solution

population mean,u = 85.3
standard deviation,sigma = 6.94

a.
P(X< 95 ) = P(Z< ((95-85.3) / 6.94)
= P(Z< 1.4)
= 0.9192
= 91.92%

b.
P( 76 <X< 88 )
= P( ((76-85.3) / 6.94) <Z< ((88-85.3) / 6.94) )
= P( -1.34 <Z< 0.39 )
= P(Z<0.39) - P(Z<-1.34)
= P(Z<0.39) - (1 - P(Z<1.34))
= 0.6517 - ( 1 - 0.9099)
= 0.6517 - 0.0901
= 0.5616
= 56.16%

c.
P(X> 70 ) = P(Z> ((70-85.3) / 6.94)
= P(Z<2.2)
= 0.9861
= 98.61%

d.
P(X> 78.5 ) = P(Z> ((78.5-85.3) / 6.94)
= P(Z> -0.98 )
= P(Z<0.98)
= 0.8365

e.
P(-k <Z< k) = 0.50
2*P(Z<k) - 1 = 0.50
P(Z<k) = 0.75
k = 0.675

u - k*sigma = 85.3 - 0.675*6.94 = 80.6155
u + k*sigma = 85.3 + 0.675*6.94 = 89.9845

range is from 80.6155 to 89.9845