Question

1. a certain type of remote - control car has a fully charged battery at the time of purchase. the distribution of running times of cars of this type, before they require recharging of the battery for the first time after its period of initial use, is approximately normal with a mean of 80 minutes and a standard deviation of 2.5 minutes. the shaded area in the figure below represents which of the following probabilities? (a) the probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 82.5 minutes. (b) the probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 85 minutes. (c) the probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 82.5 minutes. (d) the probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 85 minutes. (e) the probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 87.5 minutes.

Explanation:

Step1: Calculate lower - bound value

Given $\mu = 80$ minutes and $\sigma=2.5$ minutes. For $\mu - 2\sigma$, we substitute the values: $80-2\times2.5=80 - 5=75$ minutes.

Step2: Calculate upper - bound value

For $\mu+\sigma$, we substitute the values: $80 + 2.5=82.5$ minutes.

Step3: Interpret the shaded area

The shaded area represents the probability that the running - time of a randomly selected car is between $\mu - 2\sigma$ and $\mu+\sigma$, which is between 75 minutes and 82.5 minutes.

Answer:

A. The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 82.5 minutes.