Respuesta :
Answer:
a) 2.5%
b) 97.5%
c) 16%
d) 84%
e) 50%
f) 50%
g) 84%
h) 16%
i) 97.5%
j) 2.5%
Step-by-step explanation:
The empirical rule, or the rule of 50%-34%-14%, states that:
In a normally distributed stat with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]...
a) 2.5% of the scores are going to be above [tex]\mu + 2\sigma[/tex]
b) 13.5% of the scores are going to be above [tex]\mu + \sigma[/tex] and below [tex]\mu + 2\sigma[/tex].
c) 34% of the scores are going to be above [tex]\mu[/tex] and below [tex]\mu + \sigma[/tex]
d) 34% of the scores are going to be above [tex]\mu - \sigma[/tex] and below [tex]\mu[/tex]
e) 13.5% of the scores are going to be above [tex]\mu - 2\sigma[/tex] and below [tex]\mu - \sigma[/tex]
f) 2.5% of the scores are going to be below [tex]\mu - 2\sigma[/tex]
In this problem
We have that [tex]\mu = 80s[/tex] and [tex]\sigmma = 10s[/tex]
So:
(a) above 100, (b) below 100
[tex]100 = \mu + 2\sigma = 80 + 2*10[/tex]
So 2.5% of the scores are going to be above 100, and the other 97.5% is going to be below 100
c) above 90, (d) below 90
[tex]90 = \mu + \sigma = 80 + 10[/tex]
So 13.5% of the scores are going to be above 90 and below 100, and 2.5% of the scores are going to be above 100. So 13.5% + 2.5% = 16% of the scores are going to be above 90 and the other 84% is going to be below 90
(e) above 80, (f) below 80
80 is the mean, so approximately 50% percent of the scores are going to be above 80 and 50% are going to be below 70%.
(g) above 70, (h) below 70
[tex]70 = \mu - \sigma = 80 - 10[/tex]
34% of the scores are going to be above 70 and below 80, and other 50% percent of the scores are going to be above 80. So in all, 84% of the scores are going to be above 70. The other 16% of the scores are going to be below 70.
(i) above 60, and (j) below 60
[tex]60= \mu - 2\sigma = 80 - 2*10[/tex]
So 2.5% of the scores are going to be below 60, and the other 97.5% is going to be above 100
