Chapter 2, Problem 10CRE

To determine

To find: the mean and standard deviation of the scores

Answer to Problem 10CRE

The required mean and standard deviation are 250 and 175.78 respectively.

Explanation of Solution

Calculation:

LetXbe the scores obtained by students.

That is, $P\left(X<25\right)=0.10$ and

  $P\left(X>475\right)=0.10\Rightarrow P\left(X\le 475\right)=0.90$

The z -values corresponding to 0.10 and 0.90 are -1.28 and 1.28 respectively.

The following graph illustrates the given information to set up two equations in two unknowns.

  

Then, we can find the values of unknown mean and standard deviation using the following two equations as follows:

  $\begin{array}{l}-1.28=\frac{25-\mu }{\sigma }-----(1)\\ 1.28=\frac{475-\mu }{\sigma }-----(2)\end{array}$

Solving the above two equations, we get

  $\mu =250$

And $\begin{array}{l}\sigma =\frac{225}{1.28}\\ =175.78\end{array}$

Conclusion:

Hence, the required mean and standard deviation are 250 and 175.78 respectively.