Question

The mean age for a person getting married for the first time is 25.4 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 21.7 and 33.4 years old?

b) What is the probability that a person being married for the first time is over 29.1 years old?

c) What is the probability that a person being married for the first time is between 18.6 and 32.8 years old?

d) 85% of people getting married for the first time do so before what age?

Answer 1

a)

µ =    25.4                                  
σ =    4.9                                  
we need to calculate probability for ,                                      
P (   21.7   < X <   33.4   )                      
=P( (21.7-25.4)/4.9 < (X-µ)/σ < (33.4-25.4)/4.9 )                                      
                                      
P (    -0.755   < Z <    1.633   )                       
= P ( Z <    1.633   ) - P ( Z <   -0.76   ) =    0.9487   -    0.2251   =    0.7236   (answer)

b)

µ =    25.4                  
σ =    4.9                  
                      
P ( X ≥   29.1   ) = P( (X-µ)/σ ≥ (29.1-25.4) / 4.9)              
= P(Z ≥   0.76   ) = P( Z <   -0.755   ) =    0.2251   (answer)

c)

we need to calculate probability for ,                                      
P (   18.6   < X <   32.8   )                      
=P( (18.6-25.4)/4.9 < (X-µ)/σ < (32.8-25.4)/4.9 )                                      
                                      
P (    -1.388   < Z <    1.510   )                       
= P ( Z <    1.510   ) - P ( Z <   -1.39   ) =    0.9345   -    0.0826   =    0.8519   (answer)

d)

P(X≤x) =   0.8500                  
                      
Z value at    0.85   =   1.0364   (excel formula =NORMSINV(   0.85   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   1.036   *   4.9   +   25.4  
X   =   30.48   (answer)          
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excel formula for probability from z score is =NORMSDIST(Z)