Question

According to the Normal model ​N(0.071​,0.027​) describing mutual fund returns in the 1st quarter of​ 2013, determine what percentage of this group of funds you would expect to have the following returns. Complete parts​ (a) through​ (d) below. ​a) Over​ 6.8%? ​b) Between​ 0% and​ 7.6%? ​c) More than​ 1%? ​d) Less than​ 0%? (Please show work!)

Answer 1

Solution :

Given that ,

N(0.071​,0.027​)

mean = = 0.071 = 7.1%

standard deviation = = 0.027 = 2.7%

a) P(x > 6.8%) = 1 - p( x< 6.8% )

=1- p P[(x - ) / < (6.8% - 7.1%) / 2.7% ]

=1- P(z < -0.14)

Using z table,

= 1 - 0.4443

= 0.5557

The percentage is = 55.57%

b) P(0% < x < 7.6% ) = P[(0% - 7.1%)/ 2.1%) < (x - ) /  < (7.6% - 7.1%) / 2.7%) ]

= P( -3.38 < z < 0.19 )

= P(z < 0.19) - P(z < -3.38 )

Using z table,

= 0.5753 - 0.0004

= 0.5749

The percentage is = 57.49%

c) P(x > 1%) = 1 - p( x< 1% )

=1- p P[(x - ) / < (1% - 7.1%) / 2.7% ]

=1- P(z < -2.26)

Using z table,

= 1 - 0.0119

= 0.9881

The percentage is = 98.81%

d) P(x < 0%) = P[(x - ) / < (0% - 7.1%) / 2.7% ]

= P(z < -3.38)

Using z table,

= 0.0004

The percentage is = 0.04%