Question

On average, indoor cats live to 16 years old with a standard deviation of 2.5 years. Suppose that the distribution is normal. Let X = the age at death of a randomly selected indoor cat. Round answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N([],[])


b. Find the probability that an indoor cat dies when it is between 17.2 and 19.6 years old.[]



c. The middle 20% of indoor cats' age of death lies between what two numbers?

Low: [] years

High: [] years

Answer 1

Answer:

(a) N (16, 2.5²)

(b) 0.241

(c) Low: 15.4 years

    High: 16.6 years

Step-by-step explanation:

The random variable X is defined as the age at death of a randomly selected indoor cat.

(a)

The distribution of X is:

$X\sim N(\mu = 16, \sigma^{2}=2.5^{2})$

(b)

Compute the probability that an indoor cat dies when it is between 17.2 and 19.6 years old as follows:

$P(17.2$

                            $=P(0.48$

Thus, the probability that an indoor cat dies when it is between 17.2 and 19.6 years old is 0.241.

(c)

Compute the two numbers within which 20% of indoor cats' age of death lies as follows:

$P(x_{1}$

The corresponding value of z is, 0.25.

Compute the value of x₁ and x₂ as follows:

$z=\frac{x_{1}-\mu}{\sigma}\\\\0.25=\frac{x_{1}-16}{2.5}\\\\x_{1}=16+(0.25\times 2.5}\\\\x_{1}=16.625\\\\x_{1}\approx 16.6$                $z=\frac{x_{1}-\mu}{\sigma}\\\\-0.25=\frac{x_{2}-16}{2.5}\\\\x_{2}=16-(0.25\times 2.5}\\\\x_{2}=15.375\\\\x_{2}\approx 15.4$

Low: 15.4 years

High: 16.6 years