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
muminat
3 years ago
8

At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the n

umber of cups he sells each day is normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also believes that the number of doughnuts he sells each day is independent of the coffee sales and is normally distributed with a mean of 150 doughnuts and a standard deviation of 12. The shop is open every day but Sunday. Assuming day-to-day sales are independent, what?s the probability he?ll sell over 2000 cups of coffee in a week? If he makes a profit of 50 cents on each cup of coffee and 40 cents on each doughnut, can he reasonable expect to have a day?s profit of over $300? Explain. What?s the probability that on any given day he?ll sell a doughnut to more than half of his coffee customers?
Mathematics
1 answer:
wolverine [178]3 years ago
8 0

Answer:

(1) The probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2) The shop owner has no reasonable chance to expect earning a profit more than $300.

(3) The probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

Step-by-step explanation:

Let <em>X</em> = number of cups of coffee sold and <em>Y</em> = number of donuts sold.

The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = 320 and <em>σ </em>= 20.

The random variable <em>Y</em> follows a Normal distribution with parameters <em>μ</em> = 150 and <em>σ </em>= 12.

The shop owner opens the shop 6 days a week.

(1)

Compute the probability that the shop owner sells over 2000 cups of coffee in a week as follows:

P(X>2000)=P(\frac{X-\mu}{\sigma}>\frac{2000-(6\times320)}{6\times20})\\=P(Z>0.67)\\=1-P(Z

Thus, the probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2)

The equation representing the profit earned on selling 1 cup of coffee and 1 doughnut in a day is:

P = 0.5<em>X</em> + 0.4<em>Y</em>

Compute the probability that the shop owner earns more than $300 as profit as follows:

P(Profit>300)=P(\frac{Profit-\mu}{\sigma}>\frac{300-((0.5\times320)+(0.4\times150))}{\sqrt{0.5^{2}(20)^{2}+0.4^{2}(12)^{2}}})\\=P(Z>7.21)\\\approx0

The probability of earning a profit more then $300 is approximately 0.

Thus, the shop owner has no reasonable chance to expect earning a profit more than $300.

(3)

The expression representing the statement "he'll sell a doughnut to more than half of his coffee customers" is:

<em>Y</em> > 0.5<em>X</em>

<em>Y</em> - 0.5<em>X</em> > 0

Compute the probability of the event (<em>Y</em> - 0.5<em>X</em> > 0) as follows:

P(Y - 0.5X > 0)=P(\frac{(Y - 0.5X) -\mu}{\sigma}>\frac{0-(150-(0.5\times320}{\sqrt{12^{2}+0.5^{2}20^{2}}})\\=P(Z>0.64)\\=1-P(Z

Thus, the probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

You might be interested in
There is a bubble gum blowing contest, Mary blew 4 bubbles, Sophia blew 5 bubbles, and Jada blew 6 bubbles. If the mean in the d
Vitek1552 [10]
It would be one bubble
4 0
2 years ago
An investment of $900 earns 6% annual interest and is compounded semi-annually. Write an equation
nalin [4]

Answer:

A=900(1+\frac{0.06}{2})^{2(t)}

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

First, change 6% into a decimal:

6% -> \frac{6}{100} -> 0.06

Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:

A=900(1+\frac{0.06}{2})^{2(t)}

4 0
2 years ago
Help me with this right now please everyone
garik1379 [7]
Number 5 is 25+h divide f
8 0
3 years ago
Enter the number that belongs in the green box cd=
qwelly [4]
57 because it is right n mark ne brain list please
4 0
3 years ago
Read 2 more answers
What are the constant(s) in the expression 6y+3x-2​
Anna71 [15]

Answer:

2 is a contact but 6 and y are not because six is with y and 3 is with x

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Mr. Jones waffle recipe uses 3/4 cups of milk to make 8 waffles how many cups of milk should be used to make 24 waffles?
    9·1 answer
  • Y- (z + x - 2); use x = 4, y = 5, and z = 2<br><br> Please evaluate using the values given
    5·2 answers
  • Choose the correct simplification of (8x4y3)2. (5 points)
    5·2 answers
  • Can someone please help me!!
    8·2 answers
  • suppose you multiply a fraction Less than 1 by the mixed number 2 and 3/4 will the product be less greater or equal to 2and3/4
    14·1 answer
  • The museum guide provides 10 brochures telling about the museum's history to each tourist group. If 12 groups visited today, how
    10·2 answers
  • 6x = -24 Solve for x.
    6·2 answers
  • Which of these is an example of typing at a rate of 42 words per minute?
    8·1 answer
  • .........................................................
    9·2 answers
  • Find F(5) for the polynomial function below. <br>F(x)=4x³-12x² + 3x-3​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!