Question

. The US Marine Corps has minimum and maximum height requirements for their soldiers. Male Marines must be a minimum of 58”, and a maximum of 80”. Female Marines have the same height requirements. Data shows that the average US male is 69.1 inches in height, with a standard deviation of 2.9”, while the average US female is 63.7 inches high, with a standard deviation of 2.7 inches. What percentage of US men would qualify for the US Marines? What percent of US women would qualify

Answer 1

mu= 69.1

sigma= 2.9

X= 80

Z=(X-mu)/sigma

=(80-69.1)/2.6

=3.75862069

probability P1=P(Z<3.8276)

p1=0.999915

mu= 69.1

sigma= 2.9

X= 58

Z=(X-mu)/sigma

-3.82758

probability P2= p(Z<-3.7586)

p2= 6.4703E-05

Required probability is (P1-P2)=0.999849871

in percentage =99.9849 %

so 99.985% of US males qualify for US Marine Cops.

mu= 63.7

sigma= 2.7

X= 80

Z=(X-mu)/sigma

=(80-63.7)/2.7

=6.0370

probability P1=P(Z<6.037)

p1= 0.9999

mu= 63.7

sigma= 2.7

X= 58

Z=(X-mu)/sigma

=(58-63.7)/2.7

=-2.1111

probability P2= p(Z<-2.111)

p2= 0.017381381

Required probability is (P1-P2)=0.982618618

in percentage =98.2618 %

so 98.262 % of US Females qualify for Us Marine Cops.

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