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

See below

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