Answer:
95.4% of family vehicles is between 1 and 3 years old.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 2
Standard Deviation, σ = 6 months = 0.5 year
We are given that the distribution of age of cars is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(family vehicles is between 1 and 3 years old)
[tex]P(1 \leq x \leq 3)\\\\ = P(\displaystyle\frac{1 - 2}{0.5} \leq z \leq \displaystyle\frac{3-2}{0.5}) = P(-2 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2)\\= 0.977 -0.023 = 0.954= 95.4\%[/tex]
[tex]P(1 \leq x \leq 3) = 95.4%[/tex]
95.4% of family vehicles is between 1 and 3 years old.
