Question

The closing stock price of Ahmadi, Inc. is normally distributed with a mean of 220 dollars and a standard deviation of 20 dollars.

find:

a.The probability of a closing stock price greater than 241.25 dollars is

b.The probability of a closing stock price less than 250 dollars is

c.What percent of closing stock prices are between 180 and 220 dollars?

d.What is the minimum closing stock price of the middle 90% of the closing prices?

Answer 1

Solution :

Given that,

mean = = 220

standard deviation = = 20

a ) P (x > 241.25 )

= 1 - P (x < 241.25 )

= 1 - P ( x -  / ) < ( 241.25 - 220/ 20)

= 1 - P ( z < 21.25 / 20 )

= 1 - P ( z < 1.06)

Using z table

= 1 - 0.8554

= 0.1446

Probability = 0.1446

b) P( x < 250 )

P ( x - / ) < ( 250 - 220 / 20)

P ( z < 30 / 20 )

P ( z < 1.5)

= 0.9332

Probability = 0.9332

c ) P (180 < x < 220 )

P ( 180 - 220 / 20) < ( x -  / ) < ( 220 - 220 / 20)

P ( - 40 / 20 < z < 0 / 20 )

P (-2 < z < 0 )

P ( z < - 0 ) - P ( z < -2)

Using z table

= 0.5000 - 0.0228

= 0.4772

Probability = 0.4772

P(-z < Z < z) = 90%
P(Z < z) - P(Z < z) = 0.90
2P(Z < z) - 1 = 0.90
2P(Z < z ) = 1 + 0.90
2P(Z < z) = 1.90
P(Z < z) = 1.90 / 2
P(Z < z) = 0.95
z = 1.64 and z = - 1.64

Using z-score formula,

x = z * +

x = - 1.64 * 20 + 220

= 187.2

x = 187.2