Chapter 12.6, Problem 6PPS

a.

To determine

To calculate:

The probability that in a randomly chosen week there will be more than 20 deliveries

Answer to Problem 6PPS

The probability for a randomly chosen week which have more than 20 deliveries is $48.07\%$

Explanation of Solution

Given information:

Number of weeks having 0 to 5 deliveries is 0

Number of weeks having 6 to 10 deliveries is 9

Number of weeks having 11 to 20 deliveries is 18

Number of weeks having 21 to 25 deliveries is 12

Number of weeks having more than 26 deliveries is 13

Calculation:

The probability that a random chosen week has more than 20 deliveries can be calculated when number of weeks which have more than 20 deliveries is divisible by total number of weeks,

  $\begin{array}{l}\left(\frac{12+13}{0+9+18+12+13}\right)\times 100\%\\ =\left(\frac{25}{52}\right)\times 100\%\\ =0.4807\times 100\%\\ =48.07\%\end{array}$

Therefore, the probability for a randomly chosen week which have more than 20 deliveries is $48.07\%$

b.

To determine

To calculate:

The probability that a randomly chosen week have fewer than 21 deliveries

Answer to Problem 6PPS

The probability for randomly chosen week have fewer than 21 deliveries is $51.92\%$

Explanation of Solution

Given information:

Number of weeks having 0 to 5 deliveries is 0

Number of weeks having 6 to 10 deliveries is 9

Number of weeks having 11 to 20 deliveries is 18

Number of weeks having 21 to 25 deliveries is 12

Number of weeks having more than 26 deliveries is 13

Calculation:

The probability for randomly chosen week have less than 21 deliveries can be calculated when number of weeks having 20 or less deliveries is divisible by total number of weeks,

  $\begin{array}{l}\left(\frac{0+9+18}{0+9+18+12+13}\right)\times 100\%\\ =\left(\frac{27}{52}\right)\times 100\%\\ =0.5192\times 100\%\\ =51.92\%\end{array}$

Therefore, the probability for randomly chosen student week have less than 21 deliveries is $51.92\%$