Allie works for Canton Water Works. Her annual salary is $75,964.

At a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for revie

labwork [276]

Answer:

a. E(X) = 54.4

b. E(X) = 2.5

c. P(Y=2) = .0116

Step-by-step explanation:

a.

E(X) = np = .40 probability * 136 trials = 54.4 blocked transmissions

To get the expected value, we simply multiply probability times number of trials. You can look at it in simple terms by thinking if there's a 50% chance of flipping heads and you flip a coin twice, in an ideal world you will have .5*2 = 1 head.

b.

i. Let X represent the number of suspicious transmissions reviewed until finding the first blocked one. We will use a geometric distribution to model the "first" transmission. Whenever we're looking for the "first" time something happens, we use geometric.

ii. E(X) = 1/p , according to the geometric model.

= 1/.4 = 2.5.

We expect that the specialist will review 2.5 suspicious transactions <em>on average </em>before finding the first transmission that will be blocked.

c.

i. Let Y represent the exact number of blocked transmissions out of 10. We will use a binomial distribution to model the "fixed" number of transmissions. Whenever we're looking for a "fixed" number of times something happens, we use binomial.

ii. P(Y=k) = (n choose k)(p^k)(q^n-k)

P(Y=2) = (¹⁰₂)(.4^2)(.6^10-2)

= 45 (.4^2)(.6^10-2) = .0016

As for calculator notation, the n choose k can be accessed on a TI-84 via MATH -> PRB -> nCr. It looks like 10 nCr 2 on the display.

Hence the probability that two transactions out of ten will be blocked is .0016 by the binomial model.

5 0

2 years ago

A and b are natural numbers. The diameter of cell a is 2.3 , and the diameter of cell b is 2.3 .

Pani-rosa [81]

After clarification we see the respective diameters are

$A = 2.3 \times 10^{-a}$

$B = 2.3 \times 10^{-b}$

We're asked about the ratio

$A:B = 2.3 \times 10^{-a} : 2.3 \times 10^{-b} = 10^{-a} : 10^{-b} = 10^b : 10^a = 10^{b-a} : 1$

Now we can go through the choices.

A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.

$A:B=10^{6-4}:1 = 100:1$

It would be more proper to say the diameter of cell A is 100 times the diameter of cell B, but yes, this is TRUE.

B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.

FALSE. 10 to the minus 4 is 100 times bigger than 10 to the minus 6, so a is bigger.

C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.

FALSE. We already calculated its 100 times bigger.

D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.

FALSE.

8 0

2 years ago

Read 2 more answers

At the time of her grandson's birth, a grandmother deposits $ 2000 in an account that pays 3.5 % compounded monthly. What will

11Alexandr11 [23.1K]

At the time of her grandson's birth, a grandmother deposits $12,000.00 in an account that pays 2% compound monthly. What will be that value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawls are made during the period.
---
A(t) = P(1+(r/n))^(nt)
---
A(21) = 12000(1+(0.02/12))^(12*21)
---
A(21) = 12000(1.5214)
---
A(21) = #18,257.15

7 0

2 years ago

Read 2 more answers

Today, John ran 15 miles in 2 hours and 30 minutes. He wants to represent the relationship between the distance he ran, in miles

jeyben [28]

Answer:

d = 6t

Step-by-step explanation:

Firstly, lets change the 2 hours and 30 minutes to 2.5 hours, you could devide the time in minutes by 60 to get that number 2[hours]+( $\frac{30}{60}$ )[minutes to hours] = 2.5Hours.

Anyway, John ran 15 miles in 2.5 hours which means he ran (15÷2.5) in one hour which is equal to 6miles per hour. That means if you multiply the hours he ran by 6 you will get the miles he ran.

So the answer would be:

d = 6t

3 0

2 years ago

Identify the expression equivalent to 4(x + x + 7) − 2x + 8 − 4 by substituting x = 1 and x = 2.

miv72 [106K]

F(1)=4(1+1+7)-2(1)+8-4
f(1)=36+2
f(1)=38

f(2)=4(2+2+7)-2(2)+8-4
f(2)=44

4 0

2 years ago