Select ALL the correct answers.
2 answers:
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Answer:
1)
2) Expected number of 200 restaurants in which exactly 8 customers use the drive-through: 20.66
Expected number of 200 restaurants in which exactly 9 customers use the drive-through: 13.76
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
Question 1. Use the Poisson distribution to calculate the probability that exactly 8 cars will use the drive-through between 12:00 midnight and 12:30 AM on a Saturday night at Wendy's. Do the same for exactly 9 cars.
Cars arrive at the Wendy's drive-through at a rate of 1 car every 5 minutes between the hours of 11:00 PM and 1:00 AM. on Saturday nights. This means that during 30 minutes, 6 cars expected to arrive. So .
P(X = 8)
P(X = 9)
Question 2. At how many of the 200 restaurants in the survey would you expect exactly 8 customers to use the drive-through? exactly 9 customers?
There is a 10.33 probability that 8 customers would use the drive through for each restaurant.
So of 200, the expected number is
There is a 6.88 probability that 9 customers would use the drive through for each restaurant.
So of 200, the expected number is
Answer:
For a point defined bt a radius R, and an angle θ measured from the positive x-axis (like the one in the image)
The transformation to rectangular coordinates is written as:
x = R*cos(θ)
y = R*sin(θ)
Here we are in the unit circle, so we have a radius equal to 1, so R = 1.
Then the exact coordinates of the point are:
(cos(θ), sin(θ))
2) We want to mark a point Q in the unit circle sch that the tangent has a value of 0.
Remember that:
tan(x) = sin(x)/cos(x)
So if sin(x) = 0, then:
tan(x) = sin(x)/cos(x) = 0/cos(x) = 0
So tan(x) is 0 in the points such that the sine function is zero.
These values are:
sin(0°) = 0
sin(180°) = 0
Then the two possible points where the tangent is zero are the ones drawn in the image below.
