Question

The average size of a bank deposit account is 450 Ls with a standard deviation of 80 Ls. Assuming that the size of the deposit account has a normal distribution, determine the percentage of deposit accounts by size

a) from 200 Ls to 600 Ls;

b) more than 400 Ls.

Answer 1

Solution :

Given that ,

mean = = 450

standard deviation = = 80

a) P( 200 < x < 600 )

= P[(200 - 450)/ 80 ) < (x - ) /  < (600 - 450) / 80) ]

= P(-3.125 < z < 1.875 )

= P(z < 1.875) - P(z < -3.125)

Using z table,

= 0.9696 - 0.0009

= 0.9687

= 96.87%

Answer :- 96.87%

b) P(x > 400)

  = 1 - P( x < 400)

= 1 - P[(x - ) / < (400 - 450) / 80]

= 1 - P(z < -0.625 )

Using z table,

= 1 - 0.2660

= 0.7340

= 73.40%

Answer :- 73.40%