Project #33493 - Probability/Statistics

1.) The variance of a binomial distribution for which n = 100 and p = 0.20 is:

 

2.) The atoms of a radioactive element are randomly disintegrating. The process can be modeled with a Poisson distribution. Every gram of this element, on average, emits 3.9 alpha particles per second. Find the probability that during the next second the number of alpha particles emitted from 1 gram is:

At most 6:

Between 3 and 6 included:

 

3.) A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on a Michigan highway where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. 

What is the probability that no cars are exceeding the speed limit?

What is the probability that at least 7 cars are exceeding the speed limit?

Suppose that an highway patrol officer can obtain radar readings on 500 vehicles during a typical shift. How many traffic violations would be found in a shift?

 

4.) Consider two random variables X and Y. Suppose that the variance of X is 20, that this of Y is 10, and that the covariance of X and Y is 5. What is the variance of the random variable 2X+Y?

 

5.) Half of all newborns are girls and half are boys. Hospital A records an average of 50 births a day. Hospital B records an average of 10 births a day. On a particular day, which hospital is more likely to record 80% or more female births?

6.) A corporate executive officer is attempting to arrange a meeting of his three vice presidents for tomorrow morning. He believes that each of these three busy persons, independently of the others, has about a 60% chance of being able to attend the meeting. What is the probability that exactly two of the three vice presidents can attend the meeting?

 

Subject Mathematics
Due By (Pacific Time) 06/17/2014 0800 pm
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