Question

4. Based on data from a car bumper sticker study, when a car is randomly selected, the number of bumper stickers and the corresponding probabilities are as follows: 0 (0.797); 1 (0.099); 2 (0.036); 3 (0.017); 4 (0.013); 5 (0.011); 6 (0.009); 7 (0.007); 8 (0.006); 9 (0.005). a. Does the given information describe a probability distribution? Why or why not? b. Would it be unusual for a car to have more than two bumper stickers? Explain this!

Answer #1

Let x be the number of bumper stickers and P(x) be its corresponding probabilities.

Given probability distribution is

x | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

P(x) | 0.797 | 0.099 | 0.036 | 0.017 | 0.013 | 0.011 | 0.009 | 0.007 | 0.006 | 0.005 |

Here sum of all probabilities = 1

So the given distribution is probability distribution.

Probability that car have more than two bumper stickers

= P(X = 3) + P(X= 4) + P(X = 5) + P(X = 6) + P(X = 7) +P(X = 8) + P(X = 9)

= 0.017 + 0.013 + 0.011 + 0.009 + 0.007 + 0.006 + 0.005

= 0.068

**Probability that car have more than two bumper stickers
is 0.068**

Probability that car have more than two bumper stickers = 0.068 > 0.05.

So we can say that it is not unusual.

**It would not be unusual for a car to have more than two
bumper stickers.**

2.) When a car is randomly selected, the number of bumper
stickers and the corresponding probabilities are: 0 (0.814); 1
(0.083); 2 (0.044); 3 (0.019); 4 (0.012); 5 (0.008); 6 (0.008); 7
(0.004); 8 (0.004); 9 (0.004);
a.) Does the given information describe a probability distribution?
Explain why
b.) Assuming that a probability distribution is described, find
its mean and standard deviation.
c.) Use the range rule of thumb to identify the range values for
unusual numbers of bumper stickers....

Dupree Industries is deciding whether to automate one phase of
its production process. The manufacturing equipment has a six-year
life and will cost $915,000. Projected net cash inflows are
as?follows
Year 1
$260,000
Year 2
253,000
Year 3
227,000
Year 4
211,000
Year 5
203,000
Year 6
177,000
Requirments
1. Compute this? project's NPV using duprees 16?% hurdle rate.
Should Duprees invest in the? equipment?
2. Dupree could refurbish the equipment at the end of six years
for $104,000. The...

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