Question

4. The price of shares of Bank of Florida at the end of each trading day for the last year followed the normal distribution. The mean price was $42.00 per share and the standard deviation was $2.25.

A: What percent of the days was the price over $42.00?

b. What percent of the days was the price between $38.00 and $40.00?

c. What was the stock’s price on the highest 15% of days?

Answer 1

Solution :

Given that,

mean = = 42

standard deviation = = 2.25

P(x >42 ) = 1 - P(x<42 )

= 1 - P[(x -) / < (42-42) /2.25 ]

= 1 - P(z <0 )

Using z table

= 1 - 0.5000

=0.50

=50.00%

b

P(38< x < 40) = P[(38 - 42) /2.25 < (x - ) / < (40-42) / 2.25)]

= P( -1.78< Z <-0.89 )

= P(Z <-0.89 ) - P(Z <-1.78 )

Using z table   

= 0.1867 - 0.0375

= 0.1492

=14.92%

c

Solution:-

Given that,

Given that,

mean = = 42

standard deviation = = 2.25

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15

= P(Z < z) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z <1.04 ) = 0.85  

z =1.04

Using z-score formula,

x = z * +

x = 1.04 * 2.25+42

x = 44.34