Question

5) Scores on an English test are normally distributed with a mean of 82% and a standard deviation of 3.5%. Find the value of the third quartile.

Answer 1

Solution : Here, the given information are

$\mu$=82 , and $\sigma$ =3.5

Use the standard normal formula

Z=(x-$\mu$)/$\sigma$

Z*$\sigma$ = x-$\mu$

x=$\mu$+Z*$\sigma$

For third quartile put Z=0.675

Third quartile Q3 had 75% data,

Q3 = $\mu$ + 0.675*$\sigma$

=82+0.675*3.5

Q3 = 84.3625