Road Construction in the Town of Hiawatha Has Presented SomeLet the Random Variable K = Number of Cars Backed

The Answer is a) Graph should be consistent with these values. k P ( x ) 0 . 60 1 . 20 2 . 15 3 . 05 \begin{array} { | c | c | } \hline k & \mathrm { P } ( x ) \\\hline 0 & .60 \\\hline 1 & .20 \\\hline 2 & .15 \\\hline 3 & .05 \\\hline\end{array} k 0 1 2 3 P ( x ) .60 .20 .15 .05 b) i) 0.2 ii) 0.8 iii) 0.4

Road Construction in the Town of Hiawatha Has Presented SomeLet the Random Variable K = Number of Cars Backed

The Answer is a) Graph should be consistent with these values. k P ( x ) 0 . 60 1 . 20 2 . 15 3 . 05 \begin{array} { | c | c | } \hline k & \mathrm { P } ( x ) \\\hline 0 & .60 \\\hline 1 & .20 \\\hline 2 & .15 \\\hline 3 & .05 \\\hline\end{array} k 0 1 2 3 P ( x ) .60 .20 .15 .05 b) i) 0.2 ii) 0.8 iii) 0.4

Solved

Road Construction in the Town of Hiawatha Has Presented Some

question 3

Essay

Road construction in the town of Hiawatha has presented some problems for the
traffic engineers. Small businesses such as Joe's Barber Shop will require an
alternate entrance for their customers. This will in turn create a minor congestion of
traffic nearby because cars will be backed up and the entrance to the parking lot. The
engineers have studied the problem using simulations based on current traffic
patterns. The results from 500 trials are shown below: $\begin{array} { | c | c | } \hline \boldsymbol { k } & \begin{array} { l } \text { Number of times } \boldsymbol { k } \\\text { cars are backed up } \\\text { at the entrance }\end{array} \\\hline 0 & 300 \\1 & 100 \\2 & 75 \\3 & 25 \\\hline\end{array}$ Let the random variable k = number of cars backed up at the entrance.
a) Fill in the table below with the estimated probability distribution of k, and sketch a
probability histogram for x. Probability distribution
$\begin{array}{|l|l|}\hline k & \mathbf{P}(x) \\\hline 0 & \\\hline 1 & \\\hline 2 & \\\hline 3 & \\\hline\end{array}$

Probability histogram
$Road construction in the town of Hiawatha has presented some problems for the traffic engineers. Small businesses such as Joe's Barber Shop will require an alternate entrance for their customers. This will in turn create a minor congestion of traffic nearby because cars will be backed up and the entrance to the parking lot. The engineers have studied the problem using simulations based on current traffic patterns. The results from 500 trials are shown below: \begin{array} { | c | c | } \hline \boldsymbol { k } & \begin{array} { l } \text { Number of times } \boldsymbol { k } \\ \text { cars are backed up } \\ \text { at the entrance } \end{array} \\ \hline 0 & 300 \\ 1 & 100 \\ 2 & 75 \\ 3 & 25 \\ \hline \end{array} Let the random variable k = number of cars backed up at the entrance. a) Fill in the table below with the estimated probability distribution of k, and sketch a probability histogram for x. Probability distribution \begin{array}{|l|l|} \hline k & \mathbf{P}(x) \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{array} Probability histogram b) Using the estimated probabilities in part (a), calculate the following: i) P ( k = 1 ) , the probability that 1 car is backed up at the entrance. ii) P ( x < 2 ) , the probability that fewer than 2 cars are backed up at the entrance iii) P ( x \geq 1 ) , the probability that at least 1 car is backed up at the entrance$
b) Using the estimated probabilities in part (a), calculate the following:
i) $P ( k = 1 )$ , the probability that 1 car is backed up at the entrance.
ii) $P ( x < 2 )$ , the probability that fewer than 2 cars are backed up at the entrance
iii) $P ( x \geq 1 )$ , the probability that at least 1 car is backed up at the entrance

Definitions:

Temperature

A physical quantity that expresses the subjective perceptions of hot and cold, measured by a thermometer in units like Celsius, Fahrenheit, or Kelvin.

Temperature

A measure of the average kinetic energy of the particles in an object or system, indicating how hot or cold the object is.

Increased

Increased refers to a situation or condition becoming larger, greater, or higher in number or amount.

X-variable

An independent variable in mathematical functions and experiments that can be changed to observe its effect on the outcome.