Question

The earnings of Amazon stock are normally distributed with a mean of $90 and a standard deviation of 10.

How likely are the earnings to be below $90? ______.____ %

How likely are the earnings to be below $80?______.____ %

How likely are the earnings to be below $100?______.____ %

How likely are the earnings to be above $100?______.____ %

Answer 1

Solution :

Given that,

mean = = 90

standard deviation = = 10

A ) P( x < 90 )

P ( x - / ) < ( 90 - 90 / 10)

P ( z < 0 / 10)

P ( z < 0 )

= 0.5000

Probability = 50%

B ) P( x < 80 )

P ( x - / ) < ( 80 - 90 / 10)

P ( z < - 10 / 10)

P ( z < - 1 )

= 0.1587

Probability = 15.87%

C ) P( x < 100 )

P ( x - / ) < ( 100 - 90 / 10)

P ( z < 10 / 10)

P ( z < 1 )

= 0.8413

Probability = 84.13%

D) P (x > 100 )

= 1 - P (x < 100 )

= 1 - P ( x -  / ) < ( 100 - 90 / 10)

= 1 - P ( z < 10 / 10 )

= 1 - P ( z < 1 )

Using z table

= 1 - 0.8413

= 0.1587

Probability = 15.87%