Question

In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of 22.6 and a standard deviation of 6.8 Complete parts​ (a) through​ (d) below.

b. find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.3 and 27.9

Answer 1

$Let\, \, mean\, \, \mu =22.6\, \, and\, \, standard\, \, deviation\, \, \sigma =6.8\, \, for\, \, normal\, \, distribution$

$The\, \, probability\, \, that\, \, a\, \, randomly\, \, selected\, \, high\, \, school\, \, student\, \, test$

$has\, \, a\, \, score\, \, between\, \, 17.3\, \, and\, \, 27.9$

  $Let\, \, x_{1}=17.3\, \, and\, \, x_{2}=27.9$

  

0-2823 : 0.2823 Z=-0478 220-78

$P\left ( \frac{x_{1}-\mu }{\sigma }< z< \frac{x_{2}-\mu }{\sigma } \right )=P\left ( \frac{17.3-22.6}{6.8 }< z< \frac{27.9-22.6 }{6.8} \right )$

  $=P\left ( -0.78< z< 0.78 \right )$

   $=Area\, \, from\, \, z=0\, \, to\, \, z=-0.78\, &plus;\, area\, from\, \, z=0\, \, to\, \, z=0.78$

$=0.2823&plus;0.2823$

  $=0.5646$