Stat 104 December 11, 2017 Assistant Professor Angela Johnson-Shaw Final Examina

Question

Stat 104 December 11, 2017 Assistant Professor Angela Johnson-Shaw Final Examination Please show all work for full credit. Answer any 20 of the following 30 problems. 1. The following table lists certain values of x and its probabilities. Determine whether or not it satisfies the two conditions required for a valid probability distribution. ,36 ,48 .62 .26 2. Five percent of all cars manufactured at a large auto company are lemons. Suppose two cars are selected at random from the production line of this company. Let x denote the number of lemons in this sample. Draw a tree diagram for this problem and write the probability distribution of x. A car rental agency currently has 44 cars available, 12 of which have a GPS navigation system. One of the 44 cars are selected at random. Find the probability that this car a. Has a GPS navigation system 3. b. Does not have a GPS navigation system 4. A company has installed a generator to back up the power in case there is a power failure. The probability that there will be a power failure during a snowstorm is.30. The probability that the generator will stop working during a snowstorm is.09. What is the probability that during a snowstorm the company will lose both sources of power?

Explanation / Answer

As per the Chegg policy, we are advised to do only one question at a time so i am attempting the 1st one.

1.For any distribution to be a valid probability distribution, it must satsify the two conditions:

a) All the probabilities should be between 0 and 1, inclusive.

b) The sum of all the probabilities should be 1.

Here in the given distribution,

P(X = 5) = -0.36

Which is violating the first assumption and hence, the given distribution is not a valid probability distribution.

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