Answer to Question #214455 in Statistics and Probability for Princess

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