Question In The Screenshot

34kurt

0.0625 that's the answer

7 0

4 years ago

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

wolverine [178]

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 X = number of cups of coffee sold and Y = number of donuts sold.

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

The random variable Y follows a Normal distribution with parameters μ = 150 and σ = 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 = 0.5X + 0.4Y

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:

Y > 0.5X

Y - 0.5X > 0

Compute the probability of the event (Y - 0.5X > 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.

8 0

3 years ago

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!!

Over [174]

9514 1404 393

Answer:

b. -150

Step-by-step explanation:

We usually take elevation to be positive above sea level, and negative below sea level. If the elevation is below sea level, it is negative. If it is within 200 ft of sea level, the magnitude of the negative number is 200 or less. That is, the elevation must satisfy ...

-200 ≤ elevation < 0

The only answer choice in that range is -150.

Ethan's elevation in feet could be -150.

5 0

3 years ago

A shop sells pairs of trainers for £52 each. They make a percentage profit of 30% on each pair. What was the cost of each pair o

Sphinxa [80]

Answer:

£15.6

Step-by-step explanation:

Method 1:

You are trying to find 30% of £52.