Problem $12-17$ Using Return Distributions $[$LO$3]$

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was $6\mathrm{.}4$ percent and the standard deviation was $12\mathrm{.}4$ percent.

a$.$ What is the probability that your return on this asset will be less than $-5\mathrm{.}3$ percent in a given year? Use the NORMDIST function in Excel$$ to answer this question. $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What range of returns would you expect to see $95$ percent of the time? $($Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ What range of returns would you expect to see $99$ percent of the time? $($Enter your answers for the range from lowest to highest. A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[$a$.$ Probablility,$17\mathrm{.}36,\%,,,],[$b$.95\%$ level,$-17\mathrm{.}90,\%,$to$,30\mathrm{.}70,$