Question

Question 1

Given a normal distribution with µ=15 and σ = 5, what is the probability that

1. X>20
2. X<20
3. X<20 or X>20

INSTRUCTIONS: Show all your work as to how you have reached your answer. Please don’t simply state the results. Show graphs where necessary.

Answer 1

Solution :

Given that,

mean = = 100

standard deviation = = 15

a ) P (x > 20)

= 1 - P (x < 20 )

= 1 - P ( x -  / ) < ( 20 - 15 / 5)

= 1 - P ( z < 5 / 5 )

= 1 - P ( z < 1 )

Using z table

= 1 - 0.8413

= 0.1587

Probability =0.1587

b ) P( x < 20 )

P ( x - / ) < ( 20- 15 / 5)

P ( z < 5 / 5 )

P ( z < 1 )

= 0.8413

Probability = 0.8413

c ) P( x < 20 )

P ( x - / ) < ( 20- 15 / 5)

P ( z < 5 / 5 )

P ( z < 1 )

= 0.8413

P (x > 20 )

= 1 - P (x < 20 )

= 1 - P ( x -  / ) < ( 20- 15 / 5)

= 1 - P ( z < 5 / 5 )

= 1 - P ( z < 1)

Using z table

= 1 - 0.8413

= 0.1587

Probability = 0.8413 + 0.1587 = 1