Mathematics: (a) 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 (a) Height between 148cm and 175cm (b) Height above 164cm (c) Height below 179cm

(a) According to the Ministry of Health, the height

prin30004

28.01.2022

a) P(148

P(-1.5

b) $P(X164)=P(\frac{X-\mu}{\sigma}\frac{164-\mu}{\sigma})=P(Z\frac{164-160}{8})=P(z0.5)$

P(z0.5)=1-P(z

c) P(X

P(z

Step-by-step explanation:

Let X the random variable that represent the heights of Guinean travels , and for this case we know the distribution for X is given by:

$X \sim N(160,8)$

Where $\mu=160$ and $\sigma=8$

Part a

We are interested on this probability

P(148

We can ue the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

Using this formula we got:

P(148

And we can find this probability with this difference using the normal standard distribution or excel:

P(-1.5

Part b

$P(X164)=P(\frac{X-\mu}{\sigma}\frac{164-\mu}{\sigma})=P(Z\frac{164-160}{8})=P(z0.5)$

And we can find this probability with this difference using the normal standard distribution or excel:

P(z0.5)=1-P(z

Part c

P(X

And we can find this probability with this difference using the normal standard distribution or excel:

P(z

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