Question

Consider the normal distribution curve below:


i) For each letter a-f, provide the missing label.

ii) For each letter g-l, provide the missing percentage.

Answer 1

Answer:

See below

Step-by-step explanation:

Note: $\mu$ is the mean and $\sigma$ is the standard deviation

A is $\mu-3\sigma$, which represents 3 standard deviations below the mean

B is $\mu-2\sigma$, which represents 2 standard deviations below the mean

C is $\mu-\sigma$, which represents 1 standard deviation below the mean

D is $\mu+\sigma$, which represents 1 standard deviation above the mean

E is $\mu+2\sigma$, which represents 2 standard deviations above the mean

F is $\mu+3\sigma$, which represents 3 standard deviations above the mean

G is $2.14\%$, which represents that 2.14% of the data are between 2 and 3 standard deviations below the mean

H is $13.59\%$, which represents that 13.59% of the data are between 1 and 2 standard deviations below the mean

I is $34.13\%$, which represents that 34.13% of the data are between the mean and 1 standard deviation below the mean

J is $34.13\%$, which represents that 34.13% of the data are between the mean and 1 standard deviation above the mean

K is $13.59\%$, which represents that 13.59% of the data are between the mean and 2 standard deviations above the mean

L is $2.14\%$, which represents that 2.14% of the data are between the mean and 3 standard deviations above the mean