Question

According to the ministry of health, the height of Guinean travellers who were quarantined in Tamale for the novel coronavirus were normally distributed about a mean of 160cm and a standard deviation of 8cm. Find the probability that a traveller selected at random has

Answer 1

Let $X=$ the height of the traveller:$X\sim N(\mu, \sigma^2).$ Then $Z=\dfrac{X-\mu}{\sigma}\sim N(0,1)$

Given $\mu=160\ cm,\sigma=8\ cm$

Find the probability that a traveller selected at random has 

i) Height between 148cm and 175cm

$$P(148<X<175)=P(X<175)-P(X\leq 148)=$$

$$=P(Z<{175-160\over 8})-P(Z\leq{148-160\over 8})=$$

$$=P(Z<1.875)-P(Z\leq-1.5)\approx$$

$$\approx0.9696-0.0668=0.9028$$

ii) Height above 164cm

$$P(X>164)=1-P(X\leq 164)=1-P(Z\leq{164-160\over 8})=$$

$$=1-P(Z\leq0.5)\approx1-0.6915=0.3085$$

iii) Height below 179cm

$$P(X<179)=P(Z<{179-160\over 8})=P(Z<2.375)\approx$$

$$\approx0.9912$$