Question

A specific breed of dog is well known for how long they can live for. On average, they live for 162 months, with a standard deviation of 30 months. What percentage of dogs live for less than 144 months?

Answer 1

Answer: 27.43%

Step-by-step explanation:

Let x be a random variable representing the age of the specific breed of dogs. Since the age is normally distributed and the population standard deviation is known, we would calculate the z score by applying the formula;

z = (x - μ)/σ

where

x is the sample mean

μ is the population mean

σ is the population standard deviation

From the information given,

μ = 162

σ = 30

x = 144

By substituting these values into the formula, we have

z = (144 - 162)/30

z = - 0.6

We want to find P(x < 144). This is the area under the curve to the left of z = - 0.6 on the standard normal distribution table. By looking at z = - 0.6 on the table,

P(x < 144) = 0.2743

Thus, the probability that a dog will live for less than 144 months is 0.2743

We would convert it to percentage by multiplying by 100. We have

0.2743 x 100 = 27.43%