Question

The NiHoMah Consulting Group sent their top executive, Yuan, to investigate the safety of a proposed water taxi from Long Beach to Catalina Island. It is known that men are heavier than women on average, so a worst case situation would be to have an all male group of passengers. If he found that, nationally, the average weight of men was 175 pounds with a standard deviation of 30 pounds, help him

a. Find the probability that the weight of a randomly selected man will be greater than 172 pounds. Draw bell curves.

b. Find the probability that a randomly selected man will have a weight between 165 and 170 pounds. Draw bell curves.

Answer 1

a)

µ =    175                  
σ =    30                  
                      
P ( X ≥   172.00   ) = P( (X-µ)/σ ≥ (172-175) / 30)              
= P(Z ≥   -0.100   )

= P( Z <   0.100   ) =    0.5398   (answer)
............

b)

µ =    175                              
σ =    30                              
we need to calculate probability for ,                                  
P (   165   < X <   170   )                  
=P( (165-175)/30 < (X-µ)/σ < (170-175)/30 )                                  
                                  
P (    -0.333   < Z <    -0.167   )                   
= P ( Z <    -0.167   ) - P ( Z <   -0.333   )

=    0.4338   -    0.3694   =    0.0644

...............................

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