Question 1191028


The standard normal distribution curve in the attached graph is used to solve this question. 

<a href="https://ibb.co/103fCdC"><img src="https://i.ibb.co/103fCdC/7aaa03f4ede8309c9a4c012e61e9af2d.jpg" alt="7aaa03f4ede8309c9a4c012e61e9af2d" border="0"></a>

a.

 The value ${{{47300}}} is a standard deviation below the mean

 {{{58500-11200=47300}}}

While ${{{69700}}} is a standard deviation above the mean
 {{{58500+12000=69700}}}

 Between the first deviation below and above the mean, you have {{{34+34=68}}}% of the salary earners within this range. 

So we have {{{68}}}% of staffs earning {{{within}}} this range. 


b. 

The second standard deviation above the mean is ${{{80900}}}. 

${{{58500+11200+11200=80900 }}}

We have {{{50+13.5+2.5= 97.5}}}% earning below ${{{80900}}}. 

Therefore, {{{100-97.5= 2.5}}}% of the workers earn {{{above}}} this amount. 


c. 

From the Standard Deviation Rule, the probability is only about {{{(1 -0 .997) / 2 = 0.0015}}} that a normal value would be more than {{{3}}} standard deviations away from its {{{mean}}} in one direction or the other. 

The probability is only {{{0.0002}}} that a normal variable would be more than {{{3.5}}} standard deviations above its mean. Any more standard deviations than that, and we generally say the probability is approximately {{{zero}}}.  


so, answer is: 

a. 

{{{68}}}% of the workers will earn between ${{{47300}}} and ${{{69700}}}. 

b. 

{{{2.5}}}% of workers will earn above ${{{80900}}}


c.
 Approximately{{{ 0 }}}