What are the percentage observations for A, B, and C?

Question

Data are drawn from a bell-shaped distribution with a mean of 20 and a standard deviation of 2.

a. Approximately what percentage of the observations fall between 18 and 22? (Round your answer to the nearest whole percent.)

b. Approximately what percentage of the observations fall between 16 and 24? (Round your answer to the nearest whole percent.)

c. Approximately what percentage of the observations are less than 16? (Round your answer to 1 decimal place.)

Answer 1

A normal distribution has the following probabilities based on the standard deviation:

a) 18 - 22 is +1 and -1 standard deviations from the mean so it encompasses 34.1% + 34.1% = 68.2% or 68% (rounded to the nearest %)

b) 16 - 24 is +2 and -2 standard deviations from the mean so it encompasses 34.1% + 34.1% + 13.6% + 13.6% = 95.4% or 95% (rounded to the nearest %)

c) Less than 16 encompasses the far left side of the graph so 0.1% + 2.2% = 2.3% or 2% (rounded to the nearest %)