Question

If the mean height of a group of students equals 170cm with a standard deviation of 10 cm, then the probability that a student is between 160cm and 180cm is .

Answer 1

Mean = 170 cm

Standard deviation = 10 cm

$P(160<X<180)=P(\frac{160-170}{10}<Z<\frac{180-170}{10})$

$P(160<X<180)=P(-1<Z<1)$

From Z normal distribution table, it is found that

$P(160<x<180)=P(Z<1)-P(Z<-1)$

$P(160<x<180)=0.8413-0.1586=0.6827$