Answer to Question #216200 in Statistics and Probability for Kia

Question

The Car Repair Ratings website provides consumer reviews and ratings for garages in the United States and Canada. The time customers wait for service to be completed is one of the categories rated. The following table provides a summary of the wait-time ratings (1 = Slow/Delays; 10 = Quick/On Time) for 40 randomly selected garages located in the province of Ontario, Canada (Car Repair Ratings website, November 14, 2012) Wait-Time Rating Number of Garages 10 Develop a probability distribution for x = wait-time rating. Any garage that receives a wait-time rating of at least 9 is considered to provide outstand- ing service. Ifa consumer randomly selects one of the 40 garages for their next car service, what is the probability the garage selected will provide outstanding wait-time service?

Answer 1

The data represents 40 randomly selected garages located in the province of Ontario Canada and random variable x be the wait-time rating.

The random variable x is defines as the reflecting the known wind condition at the time of each accident is 1, 2, 3, 4 up to 10.

The probability of random variable x equal 1 is

$P(x=1) =\frac{m}{n} \\ = \frac{6}{40} \\ = 0.150$

The probability of random variable x equal 1 is 0.150.

Similarly way find other probabilities for x as random variable.

The table for probability distribution for a random variable is

Any garage that receives a wait-time rating of at least 9 is considered to provide outstanding service. If a consumer randomly selects one of the 40 garages for their next car service, the probability the garage selected will provide outstanding wait-time service is

$P(x≥ 9) = 1 -P(x<9) \\ = 1 - [P(x=1)+P(x=2) + ...+P(x=7) +P(x=8)] \\ = 1 -[0.150 +0.050 +...+ 0.10 +0.125] \\ = 1 -0.725 \\ = 0.275$