Question

Although television HDTV converters are tested before they are placed in the installer's truck, the installer knows that 20 percent of them still won't work properly. The driver must install eight converters today in an apartment building.
Required:
a. Ten converters are placed in the truck. What is the probability that the driver will have enough working converters?
b. How many boxes should the driver load to ensure a 95percent probability of having enough working converters?

Answer 1

Answer:

HDTV Converters

a. The probability that the driver will have enough working converters = 80% (100 - 20%).

b. The driver should load 10 boxes (or specifically 9.5 boxes) to ensure a 95% probability of having enough working converters.

Step-by-step explanation:

a) Data and Calculations:

Probability of HDTV converters known to not work property = 20%

This implies that 80% (100 - 20%) will work properly.

Number of converters to install today in an apartment building = 8

Number of converters placed in the truck = 10

b) The probability that the driver will have enough working converters = the probability of having properly working converters, which is 80%.  To ensure a 95 percent probability of having enough working converters, out of 10 converters, the number of boxes to load on the truck is 9.5 (10 * 95%) boxes.  Since there are no half boxes, it means that 10 boxes must be loaded, approximated to the nearest convenient number.