Answer:
a) 68%
b) 99.7%
c) 95%
Step-by-step explanation:
The mean height for an 8th grader in the State of Florida is 146 cm with a standard deviation of 8 cm. Given a normal distribution, use the Empirical Rule to interpret the data.
Empirical rule states that:
68% of data falls within 2 standard deviations from the mean - between μ – σ and μ + σ .
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
Mean = 146
Standard deviation = 8cm
a) What percent of 8th graders heights are between 138 cm and 162 cm?
146 - sx = 138cm
146 - 138 cm = 8cm
146 - 162 cm = 8cm
Hence,68% of data falls within 2 standard deviations from the mean - between μ – σ and μ + σ .
b) What percent of 8th graders heights are between 122 cm and 170 cm?
Standard deviation = 8
146 - 122 = 24 cm
146 - 170 = -24cm
24cm/8 cm = 3
Hence,99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
c) What percent of 8th graders heights are between 130 cm and 162 cm?
146 cm - 130cm = 16cm
162 cm - 146 cm = 16 cm
16cm/8cm
= 2
Hence, 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
