Answer:
0.7743
Step-by-step explanation:
Mean of age = u = 26 years
Standard Deviation = [tex]\sigma[/tex] = 4 years
We need to find the probability that the person getting married is in his or her twenties. This means the age of the person should be between 20 and 30. So, we are to find P( 20 < x < 30), where represents the distribution of age.
Since the data is normally distributed we can use the z distribution to solve this problem. The formula to calculate the z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
20 converted to z score will be:
[tex]z=\frac{20-26}{4}=-1.5[/tex]
30 converted to z score will be:
[tex]z=\frac{30-26}{4}=1[/tex]
So, now we have to find the probability that the z value lies between -1.5 and 1.
P( 20 < x < 30) = P( -1.5 < z < 1)
P( -1.5 < z < 1 ) = P(z < 1) - P(z<-1.5)
From the z-table:
P(z < 1) = 0.8413
P(z < -1.5) =0.067
So,
P( -1.5 < z < 1 ) = 0.8413 - 0.067 = 0.7743
Thus,
P( 20 < x < 30) = 0.7743
So, we can conclude that the probability that a person getting married for the first time is in his or her twenties is 0.7743
