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

(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:

(b)

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

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:

The corresponding value of z is, 0.25.

Compute the value of x₁ and x₂ as follows:

Low: 15.4 years

High: 16.6 years

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