Question

(a) According to the Ministry of Health, the height of travellers who were quarantined in Accra for 

the coronavirus were normally distributed about a mean of 170cm and a variance of 36cm. Find 

the probability that a traveller selected at random has 

i) Height between 160cm and 175cm 

ii) Height above 164cm.

iii) Height below 180 cm

Answer 1

i) $P(160<X<175)=P(\frac{160-170}{6}<Z<\frac{175-170}{6})=P(-1.67<Z<0.83)=$

$P(Z<0.83)-P(Z<-1.67)=0.7492.$

ii) $P(X>164)=P(Z>\frac{164-170}{6})=P(Z>-1)=0.8413.$

iii) $P(X<180)=P(Z<\frac{180-170}{6})=P(Z<1.67)=0.9525.$