Question

According to the Normal model

​N(0.0650.065​,0.0180.018​)

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%?

Answer 1

Solution :

Given that ,

mean = = 0.065

standard deviation = = 0.0018

a)

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

= 1 - P((x - ) / < (0.068 - 0.065) / 0.018)

= 1 - P(z < 0.167)

= 1 - 0.5663   

= 0.4337

Answer = 43.37%

(b)

P(0< x < 0.076) = P((0 - 0.065)/ 0.018) < (x - ) /  < (0.076 - 0.065) / 0.018) )

= P(-3.61 < z < 0.61)

= P(z < 0.61) - P(z < -3.61)

= 0.9463 - 0.0002

= 0.9461

Answer = 94.61%

(c)

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

= 1 - P((x - ) / < (0.01 - 0.065) / 0.018)

= 1 - P(z < -3.056)

= 1 - 0.0011   

= 0.9989

Answer = 99.89%

(d)

P(x < 0) = P((x - ) / < (0 - 0.065) / 0.018)

= P(z < -3.61)

= 0.0002

Probability = 0.02%