Question

A random value is drawn from a normally distribution population with mean 28 and standard deviation 2.

What is the probability that the value is:

a) greater than 30?

b) less than 24?

c) greater than 28?

d) equal to 27?

Answer 1

Solution :

Given that,

mean = = 28

standard deviation = = 2

(A)P(x >30 ) = 1 - P(x<30 )

= 1 - P[(x -) / < (30-28) /2 ]

= 1 - P(z <1 )

Using z table

= 1 - 0.8413

probability= 0.1587

(B)

P(X<24 ) = P[(X- ) / < (24-28) /2 ]

= P(z <-2 )

Using z table

=0.0228

probability=0.0228

(C) P(x >28 ) = 1 - P(x<28 )

= 1 - P[(x -) / < (28-28) /2 ]

= 1 - P(z <0 )

Using z table

= 1 - 0.5

probability= 0.5

(D)P(x=28 ) =0

probability=0