Question

The data represented by the graph is normally distributed and adheres to the 68-95-99.7 rule. The standard deviation of this data is , and % of the data is either less than 4.2 or more than 11.4.

Answer 1

Answer:

Standard deviation of the data is 1.6.

5% of the data is either less than 4.2 or more than 11.4.

Step-by-step explanation:

We have been given an image of normally distributed data.

We can see that mean of our given data is 7.8 and 11.4 is 2 standard deviation above the mean. So to find the standard deviation of our given data we will subtract the 7.8 form 11.4 and divide the result by 2.

$\text{Standard deviation}=\frac{11.4-7.8}{2}$

$\text{Standard deviation}=\frac{3.6}{2}$

$\text{Standard deviation}=1.8$

Therefore, the standard deviation of our given data is 1.8.

According to the 68-95-99.7 rule approximately 68% of the data is one standard deviation away from the mean. Approximately 95% of data is 2 standard deviation away from the mean. Approximately 99.9% of data is 3 standard deviation away from the mean.

We will use z-score formula to solve the second part of our given problem.

$z=\frac{x-\mu}{\sigma}$, where,

$z=\text{z-score}$,

$x=\text{Raw score}$,

$\mu=\text{Mean}$,

$\sigma=\text{Standard deviation}$.

Let us find the z-score corresponding to raw score 4.2.

$z=\frac{4.2-7.8}{1.6}$

$z=\frac{-3.6}{1.6}$

$z=-2$

So the raw score 4.2 is 2 standard deviation below mean and 11.2 is 2 standard deviation above mean. This means that we need to figure out the data above and below 2 standard deviation the mean.

Since 95% is data is 2 standard deviation away from mean, so 5% (100%-95%) data is either less than 4.2 or more than 11.4.

Answer 2

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