Question

The lifetime of a certain type of light bulb can be approximated by a normal distribution. The list

gives the number of days a bulb can last for 10 light bulbs selected at random. Find the mean and

standard deviation of the data set. Then sketch a normal curve to represent the distribution.

25, 24, 32, 16, 22, 34. 19. 27, 18, 29

Answer 1

The standard deviation of the dataset is the square root of the variance

The mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

How to determine the mean?

The dataset is given as;

25, 24, 32, 16, 22, 34. 19. 27, 18, 29

Calculate the mean using:

μ = Sum/Count

So, we have:

μ = (25+ 24+ 32+ 16+ 22+ 34+ 19+ 27+ 18+ 29)/10

Evaluate

μ = 24.6

How to determine the standard deviation?

The standard deviation is then calculated using:

$\sigma =\sqrt{ \frac{\sum(x - \mu)^2}{n}$

So, we have:

$\sigma = \sqrt{\frac{(25 - 24.6)^2 + .................. + (27- 24.6)^2 + (18- 24.6)^2 + (29- 24.6)^2}{10}}$

Evaluate

$\sigma = \sqrt{32.44}$

Evaluate the square root

$\sigma = 5.70$

Hence, the mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

Read more about variance at:

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