Question 927549
you are asked to find {{{c}}} such that, if {{{W }}}denotes the weight of a package of sugar,

{{{P(5-c < W <5+c )<=0.91}}}
Since {{{W}}} is normally distributed, transform it into a *standard* normally distributed variable, {{{Z}}}, using the formula:

Z=(W&#8722;&#956;)&#963; <=> W=Z&#963;+&#956;

where &#956;  and &#963; are the mean and std. deviation of W's distribution.

{{{P(5-c <0.03Z+5 <5+c) <=0.91}}}

{{{P(-c*0.03<Z<c*0.03)<=0.91}}}

{{{P(-c*0.03<Z<c*0.03)<=0.91}}}


Due to the symmetry of the normal curve, you can write this as

{{{P(0<Z<c*0.03)<=0.455}}}

{{{P(Z<c*0.03)-P(Z<0)<=0.455}}}

{{{P(Z<c*0.03)-0.5<=0.455}}}

{{{P(Z<c*0.03)<=0.955}}}

Referring to a z-table, you get a corresponding z-value of {{{1.70}}}

In other words,

{{{P(Z<c*0.03)<=0.955}}}  <=>  {{{P(Z<1.70)<=0.955}}}

which means {{{1.7=c*0.03}}}  => {{{c=0.051}}}