Question

If X is a normal random variable with mean u=60 and standard deviation o = 3, find

P (x > 57) =

P (x < 63) =

P ( 58 < x < 62) =

Answer 1

Solution :

Given that,

mean = = 60

standard deviation = =3

A ) P (x > 57 )

= 1 - P (x <57 )

= 1 - P ( x -  / ) < (57- 60 / 3)

= 1 - P ( z <3 / 3 )

= 1 - P ( z < 1 )

Using z table

= 1 - 0.8413

= 0.1587

Probability = 0.1587

B ) P( x < 63 )

P ( x - / ) < ( 63 - 60 / 3)

P ( z < -3 / 3 )

P ( z < - 1)

= 0.1587

Probability = 0.1587

C ) P (58 < x < 62 )

P ( 58 - 60 / 3) < ( x -  / ) < ( 62 - 60 / 3)

P ( - 2 / 3 < z < 2 / 3 )

P (-2 < z < 0.67)

P ( z < 0.67 ) - P ( z < - 2 )

Using z table

= 0.7486 - 0.0228

= 0.7258

Probability = 0.7258