Answer:
The percentage that a new car is expected to have a sticker price of between $31,600 and $40,600 is 81.86%.
Step-by-step explanation:
The random variable X is defined as the value of new cars at a local dealership.
The mean of the random variable X is, μ = $34,600 and the standard deviation is, σ = $3,000.
The random variable X is normally distributed.
Compute the probability that a new car is expected to have a sticker price of between $31,600 and $40,600 as follows:
[tex]P(31600<X<40600)=P(\frac{31600-34600}{3000}<\frac{X-u}{\sigma}<\frac{40600-34600}{3000})\\\\=P(-1<Z<2)\\\\=P(Z<2)-P(Z<-2)\\\\=0.97725-0.15866\\\\=0.81859\\\\\approx 0.8186[/tex]
The percentage is, 0.8186 × 100 = 81.86%.
Thus, the percentage that a new car is expected to have a sticker price of between $31,600 and $40,600 is 81.86%.
