Horizontal axis with 1, 2, and 3 standard deviations above the mean are 51.6, 56.2, 60.8
Horizontal axis with 1, 2, and 3 standard deviations below the mean are 42.4, 37.8, 33.2
<u>Step-by-step explanation:</u>
A data set has a normal distribution with a mean of 47 and a standard deviation of 4.6
- Mean, M ⇒ 47
- Standard deviation ⇒ 4.6
From this information, you have to scale the horizontal axis with the mean of this distribution and values at 1, 2, and 3 standard deviations above and below the mean.
Horizontal axis with 1, 2, and 3 standard deviations above the mean :
1 standard deviation above the mean ⇒ M + SD
⇒ 47 + 4.6 = 51.6
2 standard deviations above the mean ⇒ M + 2SD
⇒ 47 + (2 × 4.6) = 56.2
3 standard deviations above the mean ⇒ M + 3SD
⇒ 47 + (3 × 4.6) = 60.8
Horizontal axis with 1, 2, and 3 standard deviations below the mean :
1 standard deviation below the mean ⇒ M - SD
⇒ 47 - 4.6 = 42.4
2 standard deviations below the mean ⇒ M - 2SD
⇒ 47 - (2 × 4.6) = 37.8
3 standard deviations below the mean ⇒ M - 3SD
⇒ 47 - (3 × 4.6) = 33.2
