Answer:
(a) between 357 and 737
[tex]95\text{\%}[/tex]
(b) above 642.
[tex]16\text{\%}[/tex]
(c) below 357.
[tex]2.5\text{ \%}[/tex]
(d) between 262 and 737.
[tex]97.35\text{\%}[/tex]
Explanation:
Given that the GMAT scores are approximately normally distributed with a mean of 547 and a standard deviation of 95.
[tex]\begin{gathered} \operatorname{mean}m=547 \\ \sigma=95 \end{gathered}[/tex]
To estimate the percentage of scores that were between the given interval let us use the normal distribution curve;
Solving for the percentage;
(a) between 357 and 737
[tex]\begin{gathered} 357=547-2(95)=m-2\sigma \\ 737=547+2(95)=m+2\sigma \\ \text{ \%P=(13.5+34+13.5+34)\%} \\ \text{ \%P}=95\text{\%} \end{gathered}[/tex]
(b) above 642.
[tex]\begin{gathered} 642=547+94=m+\sigma \\ P(>m+\sigma)=(13.5+2.35+0.15)\text{ \%} \\ P(>m+\sigma)=16\text{ \%} \end{gathered}[/tex]
(c) below 357.
[tex]\begin{gathered} 357=m-2\sigma \\ P((d) between 262 and 737. %[tex]\begin{gathered} 262=547-3(95)=m-3\sigma \\ 737=m+2\sigma \\ P(262\text{ to 737)}=(2.35+13.5+34+34+13.5)\text{\%} \\ P=97.35\text{\%} \end{gathered}[/tex]
