1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kogti [31]
3 years ago
8

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

ay nights. Wendy's begins an advertising blitz that touts its late-night drive-through service and convenience. After one week of advertising, the Wendy's marketing department conducts a survey at 200 Wendy's to count the number of cars, X, that arrive at the drive-through between the hours of 12:00 midnight and 12:30 AM on Saturday night.
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.

P(X = 8) (use 4 decimal places)
P(X = 9) (use 4 decimal places)

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?

expected number of 200 restaurants in which exactly 8 customers use the drive-through.
expected number of 200 restaurants in which exactly 9 customers use the drive-through.
Mathematics
1 answer:
mestny [16]3 years ago
8 0

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

You might be interested in
A swimming pool can be filled in 18 hours if water enters through a pipe​ alone, or in 25 hours if water enters through a hose a
pychu [463]
I am not sure, but this is what I got:
 <span>Pipe ALONE = 18 hours 

Pipe ALONE in 1 hour = 1/18 of the pool 

Hose ALONE in 1 hour = 1/25 of the pool 

TOGETHER in 1 HOUR = 1/18 +1/25 = 43/450 

TOGETHER they will fill the pool in 450/43 hours 

So 5/6 of the pool will take 5/6 X 450/43 = 2250/ 258 = 8.7209302 hours OR 

8 hours AND 43.26 minutes ANSWER
</span>
Hope this helps!


6 0
3 years ago
John made a rectangle pen for his dog using 28 feet of fencing. If the width of the pen is 2 feet more than one-half the length,
kati45 [8]
Okay, so you know that the perimeter of the pen is 28 feet. Now we need the separate side lengths.

P = 28 ft.
Length = x
Width = (1/2)x + 2

So now we can plug in the little equations of length and width into a perimeter formula:
 2(x) + 2((1/2)x + 2) = 28
Distribute the 2's and solve as needed.
2x + x + 4 = 28
3x + 4 = 28
3x = 24
x = 8

To find the width, just plug in 8 for x in our little equation:
(1/2)(8) + 2
= 6

So, the length is 8 feet and the width is 6 feet.
5 0
3 years ago
Read 2 more answers
You have two cats. Each cat has a litter of K kittens. Write an expression that describes a total number of cats and kittens you
elena-14-01-66 [18.8K]
2xk=24
K=12
Hope that makes sense
3 0
3 years ago
Simplify 2x - 8x - 6y + 9 -14 + x + 11y.
raketka [301]
We can see that 2x - 8x + x = -5x
and -6y + 11y = 5y
and 9 - 14 = -5
so simplified, it is -5x + 5y - 5
8 0
2 years ago
Read 2 more answers
The function c(m)=1.45m+3.50 represents the cost of a taxi for m miles. What does c(7) represent?
ladessa [460]
The answer is c(7)=13.65
3 0
3 years ago
Other questions:
  • Can you help me with number 4 A-D plz
    10·1 answer
  • A graphic artist earns $22 an hour and she works 40 hours a week. What is her weekly wage
    5·2 answers
  • (please zoom / zoom out if needed to see question. (: ) (Worth 10 Points Each)
    12·2 answers
  • You have two spheres. Sphere a has radius ra and sphere b has radius rb = kra. What is b's volumevb intermsofva andk? Vb = va
    11·1 answer
  • A system of equations is shown:
    9·1 answer
  • A stack of 9 different cards are shuffled and spread out face down. If 4 cards are tired face up, how many different 4-card comb
    11·1 answer
  • The price of a holiday was decreased by 12% to £600. What was the price before the decrease? Give your answer to the nearest pen
    15·2 answers
  • Someone please help me this will be a lot of points and I will follow u and Mark u the brainiest​
    10·1 answer
  • Help pls show work if needed
    10·1 answer
  • Please help me with maths​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!