Answer:
a) the proportion is 0.159 (15.9%)
b) the proportion is 0.524 (52.4%)
c) Ralph is 70.958 inches tall
Step-by-step explanation:
defining our random variable X= heights of men , then we can define the standard random variable Z as
Z= (X- μ)/σ , where μ is the population's mean and σ is the corresponding standard deviation of X
then for X=72
Z= (X- μ)/σ
Z= (72-68)/4 = 1
a) P(X> 72) = P(Z> 1) = 1-0.841 = 0.159 (using standard normal distribution tables)
b) for X=64 and X=74
Z₁= (64 -68)/4 = -1
Z₂= (74-68)/4 = 1.5
then
P(68<X< 74) = P(-1<Z <1.5) 0 = P(Z<1.5) - P(Z<-1) = 0.933- 0.159 =0.774
c) Z₃ = 0.933 - 0.774*0.25 = 0.7395
thus
Z₃= (X₃- μ)/σ →X₃ =μ+ Z₃*σ = 68 + 0.7395*4 = 70.958 inches
therefore Ralph is 70.958 inches tall
