Weights of female cats of a certain breed are normally distributed with mean 4.1 kg and standard deviation 0.6 kg.

A) Six female cats are chosen at random. What is the probability that exactly one of them weighs more than 4.5 kg?

Answer :

Given :

Given Data :

The population mean $(\mu )=4.1$

The population standard deviation $(\sigma )=0.6$

Solution :

A) If a cat is chosen at random, the probability that she weighs more than 4.5 kg :

$$\text{P}(x>4.5)=\text{P}(\frac{x–\mu }{\sigma }>\frac{4.5–4.1}{0.6})$$ $$=\text{P}(z>0.667)$$ $$=1–\text{P}(z<0.667)$$ $$=1–0.7476$$ $$=0.2524$$