Answer to Question #120101 in Statistics and Probability for Daniel Mensah

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

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

$$\approx0.9912$$