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%