Question

According to the Normal model ?N(0.054?,0.015?) 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%?

A) The expected percentage of returns that are over 6.8% is ______%

b) The expected percentage of returns that are between 0& and 7.6% is ____%

C) The expected percentage of returns that are more than 1% is ____%

D) The expected percentage of returns that are less than 0% is ____%

Type an intenger or a decimal rounded to one decimal place as needed.

Answer 1

Solution :

Given that ,

mean = = 0.054

standard deviation = = 0.015

(a)

P(x > 0.068) = 1 - P(x < 0.068)

= 1 - P((x - ) / < (0.068 - 0.054) / 0.015)

= 1 - P(z < 0.93)

= 1 - 0.8238

= 0.1762

Answer = 17.6%

(b)

P(0 < x < 0.076)

= P((0 - 0.054)/ 0.015) < (x - ) /  < (0.076 - 0.054) / 0.015) )

= P(-3.6 < z < 1.467)

= P(z < 1.467) - P(z < 3.6)

= 0.9288 - 0.0002

= 0.9286

Answer = 92.9%

(c)

P(x > 0.01) = 1 - P(x < 0.01)

= 1 - P((x - ) / < (0.01 - 0.054) / 0.015)

= 1 - P(z < -2.93)

= 1 - 0.0017

= 0.9983

Answer = 99.8%

(d)

P(x < 0) = P((x - ) / < (0 - 0.054) / 0.015)

= P(z < -3.6)

= 0.0002

Answer = 0.02%