Question

can u help pls n make it neat bc :))

Answer 1

Answer:

(a)26.1 bulb per month on average

(b)6.5

Explanation:

The number of burnt bulbs recorded over 10 months is given below:

$23,25,21 , 33,17,39,26,24,31,22$

Part A

To find the average, add up all the numbers and divide by 10.

$\begin{gathered} \text{Average}=\frac{23+25+21 + 33+17+39+26+24+31+22}{10} \\ =\frac{261}{10} \\ =26.1 \end{gathered}$

The average number of bulbs that burn out each month is 26.1.

Part B

To find the standard deviation, we use the formula below:

$\begin{gathered} \text{Standard Deviation}=\sqrt[]{\frac{\sum (x-\bar{x})^2}{n-1}} \\ \bar{X}=26.1 \end{gathered}$

The data is presented in the table below:

From the table above:

$\sum (x-\bar{x})^2=378.9$

Therefore:

$\begin{gathered} \text{Standard Deviation}=\sqrt[]{\frac{\sum (x-\bar{x})^2}{n-1}}=\sqrt[]{\frac{378.9}{10-1}} \\ =\sqrt[]{\frac{378.9}{9}} \\ =\sqrt[]{42.1} \\ =6.5\text{ (to 1 decimal place)} \end{gathered}$

The standard deviation is 6.5.