Respuesta :
Solution:
[tex]Z score =\frac{X-\sigma}{\mu}[/tex]
1. For Best Actor
[tex]X_{1}[/tex]= 59 years
[tex]\sigma=7.3, \mu=42.0[/tex]
Z, Score for best actor named, [tex]Z_{1}[/tex]
[tex]Z_{1}=\frac{59-7.3}{42}\\\\Z_{1}= \frac{51.7}{42}\\\\Z_{1}=1.23095\\\\ Z_{1}=1.24[/tex]
Z-Score for best actor = 1.24
2. Z , Score for best supporting actor , called [tex]Z_{2}[/tex]
[tex]X_{2}[/tex]=49 years
[tex]\sigma=15, \mu=49.0[/tex]
[tex]Z_{2}=\frac{49-15}{49}\\\\Z_{2}= \frac{34}{49}\\\\Z_{2}=0.6938\\\\ Z_{2}=0.70[/tex]
Z-Score for best supporting actor = 0.70
Z-Score is usually , the number of standard deviations from the mean a point in the data set is.
3. As, [tex]Z_{1}=1.24[/tex]
So, we can say that,Option (B) The Best Actor was more than 1 standard deviation above is not unusual.
4.As, [tex]Z_{2}=0.70[/tex]
So, we can say that,Option(A) The Best Supporting Actor was less than 1 standard deviation below, is not unusual.
