Question

A particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. Assume that 10 mornings are considered in this experiment.

(a) What is the probability that the light is green on exactly one morning? (b) What is the probability that the light is green on at least two mornings? (c) What is the mean number of mornings that the light is green when you approach it?

Answer #1

Suppose at a particular traffic light junction, the traffic is
green 60 % of the time, red
30 % of the time and yellow 10 % of the time. Given that a car
approaches this traffic
light junction once each day. Let X denotes the number of days that
pass up to and
including the first time the car encounters a red light. Assume
that each day represents
an independent trial.
(i) Apply a suitable model and compute the probability...

A traffic light at a certain intersection is green 45% of the
time, yellow 10% of the time, and red 45% of the time. A car
approaches this intersection once each day. Let Y denote
the number of days up to and including the third day on which a red
light is encountered. Assume that each day represents an
independent trial.
Find ?Y .

what if you encounter one traffic light on your commute to class
each day. You have determined that the probability that this light
will be red is 1/3. Which of the following is not a correct
interpretation of this probability?
a.Each time you approach the light on your commute, the
probability of it being red is 1/3.
b.The light will always be red one out of every three times that
you encounter it.
c.In the long run, the light should...

John drives and there are traffic lights on his routes. When all
traffic lights on his route are green, the entire trip takes 18
minutes. JohnŠs route includes 5 traffic lights, each of which is
red with probability 1/3, independent of every other light. Each
red traffic light that he encounters adds 1 minute to his commute.
(a) Find the expectation, and variance of the length (in minutes)
of John’s commute. (b) What is the pmf of the length (in...

Suppose that 20% of coffee drinkers have their morning cup of
coffee at home (as opposed to having it outside home). A random
sample of 20 coffee drinkers is randomly selected. Suppose you have
verified this is a Binomial experiment.
1-Identify the number of individual trials.
2-Define the binomial random variable X, in the context of
question.
3-What is the probability that exactly 4 of the 20 randomly
selected coffee drinkers have their morning cup of coffee at
home?
4-What...

Suppose you have five marbles in a bag, three green (G1, G2,
G3) and two red (R1 and R2). You conduct an experiment where you
continue to select colored marbles one at a time at random from the
bag. You stop selecting marbles when you select a
red marble. Without replacement.
Display the possible outcomes in a tree diagram.
Let x denote the discrete random variable that
represents the total number of green marbles that can be selected
before a...

Please answer with method or formula used.
A) Puenaa is getting married tomorrow, at an outdoor ceremony in
the desert. In recent years, it has rained only 5 days each year.
Unfortunately, the weatherman has predicted rain for tomorrow. When
it actually rains, the weatherman correctly forecasts rain 90% of
the time. When it doesn't rain, he incorrectly forecasts rain 10%
of the time. What is the probability that it will rain on the day
of Puenaa's wedding?
B) A...

A busy commuter is concerned about the time she spends in
traffic getting to the office. She times the drive for a couple
weeks and find that it averages 40 minutes. The next day, she tries
public transit and it takes 45 minutes. The next day she's back on
the roads, convinced that driving is quicker. However, data from
one day is not representative of variation in public transit time.
If the busy commuter decides to do more testing, how...

Suppose each time a potential customer visits your website on a
weekday there is a 25% chance they purchase something. Every hour
you get exactly 20 potential customers visiting your website.
Suppose that all website visits are independent. What is the
probability that you make 5 or less sales in an hour? What is the
expected number of sales from your website in a 10 hour time
period? Suppose on weekends the probability a visitor makes a
purchase is 0.63...

1. Decide (write yes or no) whether the experiments are binomial
experiments or not. Explain why or why not using a complete
sentence:
a) You spin a number wheel that has 20 numbers 500 times. The
random variable represents the number that is spun.
b) Surveying 300 prisoners to see whether or not they are
serving time for their first offense. The random variable
represents the number of prisoners serving time for their first
offense. Assume each prisoners response is
independent....

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