Which equation has a solution of x = 2? Choose ALL that apply.

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 Saturd

mestny [16]

Answer:

1) $P(X = 8) = 0.1033$

$P(X = 9) = 0.0688$

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ 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 $\mu = 6$ .

P(X = 8)

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 8) = \frac{e^{-6}*(6)^{8}}{(8)!} = 0.1033$

P(X = 9)

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 9) = \frac{e^{-6}*(6)^{9}}{(9)!} = 0.0688$

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

$E(X) = 200*0.1033 = 20.66$

There is a 6.88 probability that 9 customers would use the drive through for each restaurant.

So of 200, the expected number is

$E(X) = 200*0.0688 = 13.76$

8 0

3 years ago

Correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

klasskru [66]

F(x)=25-x^2
g(x)=x+5

f/g(x)=(25-x^2)/(x+5)

f(x) is in binomial form so 25-x^2 can also be written as (5-x)(5+x)

so

f/g(x)=(5-x)(5+x)/(x+5)
f/g(x)=5-x

5 0

3 years ago

Find the solution of this system of equations. -x - 5y= 30, 10x + 5y= -75

madreJ [45]

Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

------------------

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

7 0

2 years ago

When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial

Serjik [45]

Answer:

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

Step-by-step explanation:

For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability of an individual blood sample testing positive for the virus is 0.06.

This means that $p = 0.06$

If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.

It will be positive if at least one of the tests is positive, that is:

$P(X \geq 1) = 1 - P(X = 0)$