Question

1. A population is normally distributed with a mean of 18 and a standard deviation of 2.5.

What is the probability of randomly selecting one item from the population having:

a) A value greater than 18.

b) A value between 14 and 21.

Answer 1

Solution :

Given that ,

mean = = 18

standard deviation = =2.5

a) P(x >18 ) = 1 - p( x<18 )

=1- p [(x - ) / < (18 -18) /2.5 ]

=1- P(z < 0)

= 1 - 0.50 = 0.5

probability = 0.5000

b)

P( 14< x < 21) = P[(14 -18)/2.5 ) < (x - ) /  < (21-18) /2.5 ) ]

= P( -1.6< z <1.2 )

= P(z <1.2 ) - P(z <-1.6 )

Using standard normal table

= 0.8849- 0.0548 = 0.8301

Probability = .8301