Mathematics, 21.05.2020 06:05 gabrielolivas59

An online retailer has determined that the average time for credit card transactions to be electronically approved is 1.8 seconds. (Round your answers to three decimal places.) (a) Use an exponential density function to find the probability that a customer waits less than a second for credit card approval. (b) Find the probability that a customer waits more than 3 seconds. (c) What is the minimum approval time for the slowest 5% of transactions

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Answer from: anamatiascamaja

a) 0.426 = 42.6% probability that a customer waits less than a second for credit card approval.

b) 0.189 = 18.9% probability that a customer waits more than 3 seconds.

c) The minimum approval time for the slowest 5% of transactions is 5.39 seconds.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

An online retailer has determined that the average time for credit card transactions to be electronically approved is 1.8 seconds.

This means that $m = 1.8, \mu = \frac{1}{1.8} = 0.5555$

(a) Use an exponential density function to find the probability that a customer waits less than a second for credit card approval.

This is $P(X \leq 1)$ .

$P(X \leq 1) = 1 - e^{-0.5555*1} = 0.426$

0.426 = 42.6% probability that a customer waits less than a second for credit card approval.

(b) Find the probability that a customer waits more than 3 seconds.

This is P(X > 3).

$P(X x) = 1 - P(X \leq 3) = 1 - (1 - e^{-0.5555*3}) = 0.189$

0.189 = 18.9% probability that a customer waits more than 3 seconds.

This is x for which $P(X \leq x) = 0.95$

$P(X \leq x) = 1 - e^{-\mu x}$

$0.95 = 1 - e^{-0.5555x}$

$e^{-0.5555x} = 0.05$

$\ln{e^{-0.5555x}} = \ln{0.05}$

$-0.5555x = \ln{0.05}$

$x = -\frac{\ln{0.05}}{0.5555}$

x = 5.39

The minimum approval time for the slowest 5% of transactions is 5.39 seconds.

Answer from: Quest

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

#10 can anyone solve this for will give !

Answer from: Quest

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

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An online retailer has determined that the average time for credit card transactions to be electroni...