Respuesta :
Answer:
a) 95% percentage of people has an IQ score between 80 and 120.
b) 68% percentage of people has an IQ score between 90 and 110.
c) 2.5% percentage of people has an IQ score greater than 120.
Step-by-step explanation:
The empirical formula states that:
- The empirical rule is known as the three-sigma rule or 68-95-99.7 rule.
- It is a rule which states that for a normal distribution, almost all data falls within three standard deviations of the mean.
- 68% of data falls within the first standard deviation that is [tex]\mu \pm \sigma[/tex]
- 95% of data falls within the second standard deviation that is [tex]\mu \pm 2\sigma[/tex]
- 99.7% of data falls within the third standard deviation that is [tex]\mu \pm 3\sigma[/tex]
a) percentage of people has an IQ score between 80 and 120
(80, 120) can be written as:
[tex](80, 120) = (100-2(10), 100 + 2(10))\\= (\mu \pm 2\sigma)[/tex]
Thus, it is the interval within two standard deviation from the mean.
Thus, by empirical formula, 95% percentage of people has an IQ score between 80 and 120.
b) percentage of people has an IQ score between 90 and 110
(90, 110) can be written as:
[tex](90, 110) = (100-1(10), 100 + 1(10))\\= (\mu \pm 1\sigma)[/tex]
Thus, it is the interval within one standard deviation from the mean.
Thus, by empirical formula, 68% percentage of people has an IQ score between 90 and 110.
c) P(score greater than 120)
= 1 - percentage of score less than 80 - percentage of score between 80 and 120
[tex]= 1 - (95\% + 2.5\%) = 2.5\%[/tex]
From empirical formula,
2.5% percentage of people has an IQ score greater than 120.
