A certain characteristic in a large population has a distribution that is symmetric about the mean m. 84 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 9.2 years and the standard deviation is 3.5 years, what percent of the distribution has more than 12.7 years as a shelf’s average life?
Choose the correct option:
A) 18%
B) 19%
C) 20%
D) 21%
E) 22%
Average = 9.2   SD = 3.5   9.2 - 3.5 &lt; 84% of distribution &lt; 9.2 + 3.5   5.7 &lt; 84% of distribution &lt; 12.7   42% is outside this range.   Given: Distribution is symmetric. So 21% of distribution is less than 5.7 and the other 21% of distribution is greater than 5.7.   Answer: 21%
<result>D</result>
A certain characteristic in a large population has a distribution that is symmetric about the mean m. 84 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 9.2 years and the standard deviation is 3.5 years, what percent of the distribution has more than 12.7 years as a shelf’s average life?