Convert 36 4/9 to an improper fraction. Use this rule: a b/c = ac + b/c
-36 × 9 + 4/9 - (-10 2/9) - 18 2/9
Simplify 36 × 9 to 324
- 324 + 4/9 - (-10 2/9) - 18 2/9
Simplify 324 + 4 to 328
- 328/9 - (-10 2/9) - 18 2/9
Convert 10 2/9 to an improper fraction. Use this rule: a b/c = ac + b/c.
-328/9 - (- 10 × 9 + 2/9) - 18 2/9
Simplify 10 × 9 to 90
-328/9 - (- 90 + 2/9) - 18 2/9
Simplify 90 + 2 to 92
- 328/9 - (-92/9) - 18 2/9
Convert 18 2/9 to an improper fraction. Use this rule: a b/c = ac + b/c.
-328/9 - (- 92/9) - 18 × 9 + 2/9
Simplify 18 × 9 to 162
-328/9 - (- 92/2) - 162 + 2/9
Simplify 162 + 2 to 164
-328/9 - (- 92/9) - 164/9
Simplify brackets
-328/9 + 92/9 - 164/9
Join the denominators
-328 + 92 - 164/9
Simplify
-400/9
Convert to a mixed fraction
Answer:
84%
Step-by-step explanation:
The empirical rule tells you that 68% of the standard normal distribution is within 1 standard deviation of the mean. The distribution is symmetrical, so the amount in the lower tail is (1 -68%)/2 = 16%.
Since the number you're interested in, 240, is one standard deviation above the mean (200 +40), the percentage of interest is the sum of the area of the central part of the distribution along with the lower tail:
68% + 16% = 84%.
