Question

The mean age for a person getting married for the first time is 27.3 years. Assume the ages for first marriages are normal with a standard deviation of 4.9 years. (Give probability answers to four decimal places.)

a) What is the probability that a person being married for the first time is between 23.6 and 31.7 years old?

b) What is the probability that a person being married for the first time is over 33.1 years old?

c) What is the probability that a person being married for the first time is between 25.4 and 33.8 years old?

d) 75% of people getting married for the first time do so before what age?

Answer 1

a)

µ =    27.3          
σ =    4.9          
we need to calculate probability for ,              
P (   23.6   < X <   31.7   )
=P( (23.6-27.3)/4.9 < (X-µ)/σ < (31.7-27.3)/4.9 )              
              
P (    -0.755   < Z <    0.898   )
= P ( Z <    0.898   ) - P ( Z <   -0.76   ) =
0.8154   -    0.2251   =    0.5903

b)

µ =    27.3                  
σ =    4.9                  
                      
P ( X ≥   33.1   ) = P( (X-µ)/σ ≥ (33.1-27.3) / 4.9)              
= P(Z ≥   1.18   ) = P( Z <   -1.184   ) =    0.1183   (answer)

c)
µ =    27.3          
σ =    4.9          
we need to calculate probability for ,              
P (   25.4   < X <   33.8   )
=P( (25.4-27.3)/4.9 < (X-µ)/σ < (33.8-27.3)/4.9 )              
              
P (    -0.388   < Z <    1.327   )
= P ( Z <    1.327   ) - P ( Z <   -0.39   ) =
0.9077   -    0.3491   =    0.5586

d)

µ=   27.3  
σ =    4.9  
P(X≤x) =   0.75  
      
z value at 0.75=   0.6745   (excel formula =NORMSINV(0.75))
z=(x-µ)/σ      
so, X=zσ+µ=   0.674   *4.9+27.3
X =   30.605   (answer)

Please let me know in case of any doubt.

Thanks in advance!

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