Question

1. the weights of siamese cats are normally distributed with a mean of 6.4 pounds and a standard - deviation of 0.8 pounds. if a breeder of siamese cats has 128 in his care, how many can be expected to have weights between 4.8 and 7.2 pounds?

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set.
For $x = 4.8$, $z_1=\frac{4.8 - 6.4}{0.8}=\frac{- 1.6}{0.8}=-2$.
For $x = 7.2$, $z_2=\frac{7.2 - 6.4}{0.8}=\frac{0.8}{0.8}=1$.

Step2: Find probabilities

Using the standard normal distribution table, the probability corresponding to $z=-2$ is $P(Z < - 2)=0.0228$, and the probability corresponding to $z = 1$ is $P(Z < 1)=0.8413$.
The probability that $-2

Step3: Calculate expected number

The breeder has $n = 128$ cats. The expected number of cats with weights between 4.8 and 7.2 pounds is $n\times P(-2 < Z < 1)=128\times0.8185 = 104.768\approx105$.

Answer:

105