Respuesta :
Answer:
99.85%
Step-by-step explanation:
The Empirical rule formula states that
1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
3) 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the above question, we are told that
mean = 2.61
Standard deviation = 0.45
We start with the first rule
1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
μ - σ
2.61 - 0.45
= 2.16
μ + σ
2.61 + 0.45
= 3.05
We try the second rule
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
μ - 2σ
2.61 - 0.45 × 2
= 1.71
μ + 2σ
2.61 + 0.45 × 2
= 3.51
3) We try the 3rd rule
3) 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
μ - 3σ
2.61 - 0.45 × 3
= 1.26
μ + 3σ
2.61 + 0.45 × 3
= 3.96
Finally from the 3rd rule, we can see that 99.7% of the students have grades that fall between 1.26 and 3.96
The question asks us to find the percentage of students that have grade points that are at least 3.96
This means students with grade points equal to or greater that 3.96(≥)
Hence,
For students with grade points = 3.96
= 99.7%
For students with grade points more than 3.96
= 100 - 99.7%/2
= 0.3/2
= 0.15%
Therefore, percentage of the students have grade point averages that are at least 3.96 is
100% - 0.15%
= 99.85%
