The data records the smiling times, in seconds, of an eight-week-old baby. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. This means that any smiling time from zero to and including 23 seconds is equally likely. What is the probability that a randomly chosen eight-week-old baby smiles between two and 18 seconds?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
1. The data records the smiling times, in seconds, of an eight-week-old baby. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. This means that any smiling time from zero to and including 23 seconds is equally likely. What is the
2. Given a random variable X having a
a.less than 4 have 3 or more cars?
b. at least 4 have 3 or more cars?
3. A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state?
4. A production of 20 fuses is received by the store. It is known that 4 of the fuses are defective. The quality control engineer randomly selected three of the fuses from the production run. Find the probability that two of the fuses selected are defective.
5. If 7 cards are dealt from an ordinary deck of 52 playing cards, what is the probability that
a.exactly 2 of them will be face cards?
b. at least 1 of them will be a queen?
6. It is estimated that 4000 of the 10,000 voting residents of a town are against a new sales tax. If 15 eligible voters are selected at random and asked their opinion, what is the probability that at most 7 favor the new tax?
7. Find the probability that a person flipping a coin gets a.the third head on the seventh flip
b. the first head on the fourth flip.
8. On average a certain intersection results in 3 traffic accidents per month. What is the probability that for any given month at this intersection
a.exactly 5 accidents will occur?
b. less than 3 accidents will occur?
c.at least 2 accidents will occur?
9. If new cases of West Nile in New England are occurring at a rate of about 2 per month, then what’s the probability that exactly 4 cases will occur in the next 3 months?
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