Chapter 12.5, Problem 3CYU

a)

To determine

To find : Percent of class excepted to score between $19$ and $23$.

Answer to Problem 3CYU

  $\text{68\%}$

Explanation of Solution

Given Information :

Mr. Bash gave a quiz in his social studies class. Score were normally distributed.

Mean = $21$ , Standard deviation $\sigma =2$

Calculate :

Using Empiral Rule

  $\text{19}$ is $\text{1}\sigma$ away = $\text{34\%}$ values

  $\text{23}$ is $\text{1}\sigma$ away = $\text{34\%}$ values

Total = $\text{34 + 34 = 68\%}$

  $\text{68\%}$ of class is expected to score in between $\text{19}$ and $\text{23}$.

  

b)

To determine

To find : Percent of class expected to score in between $23$ and $25$.

Answer to Problem 3CYU

Explanation of Solution

Given Information :

Mean = $21$ and $5.0,\sigma =2$

Calculation :

Using Empirical Rule,

  $\text{23}$ is $\text{1}\sigma$ away = $\text{34\%}$ values

  $\text{25}$ is $\text{2}\sigma$ away = $\text{13}\text{.5\%}$ values

Total = $\text{34 + 13}\text{.5 = 47}\text{.5\%}$

c)

To determine

To find : Percent that a student scored between $17$ and $25$.

Answer to Problem 3CYU

  $\text{97\%}$

Explanation of Solution

Given Information :

  $\mu =21,\sigma =d$

Calculation :

  $17$ is $2\sigma$ = $13.5\%$ values

  $19$ is $1\sigma$ = $34\%$ values

  $21$ is mean = $34\%$ values

  $23$ is $1\sigma$ = $13.5\%$ values

  $25$ is $2\sigma$ = $2\%$ values

Probability that a student score in between $\text{17}$ and $\text{25}$ is

  $(13.5+34+34+13.5+2)=97\%$