Q.66 - The Practice of Statistics for AP

Question

The standard deviation of the average scores you get should be close to

(a) $114$.

(b) $114/100=1.14$.

(c) $114/\sqrt{100}=11.4$.

(d) $1$ .

(e) none of these.

Step-by-Step Solution

Answer

The average score's standard deviation is $11.4$.

The correct answer is (c).

Step 1: Given Information

Mean $=515$.

Standard deviation $=114$.

Number of students for SRS $=100$.

Step 2: Explanation

Assume the mean and standard deviation are $\mu$ and $\sigma$, respectively.

$\mu =515$ and

 $\sigma =114$

Use the formula to calculate the average score's standard deviation. ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$.

Substitute $114$ for $\sigma$ and $100$ for $n$ :

${\sigma }_{\overline{x}}=\frac{114}{\sqrt{100}}$

$=\frac{114}{10}$

$=11.4$

The average score's standard deviation is $11.4$.