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IgorC [24]
3 years ago
7

Calculus Question, just the first line. Other stuff is just my work...

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0
What are you even asking us
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The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a m
castortr0y [4]

Answer:

a) 50.34% probability that the arrival time between customers will be 7 minutes or less.

b) 24.42% probability that the arrival time between customers will be between 3 and 7 minutes

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}

Mean of 10 minutes:

This means that m = 10, \mu = \frac{1}{10} = 0.1

A. What is the probability that the arrival time between customers will be 7 minutes or less?

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

P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034

50.34% probability that the arrival time between customers will be 7 minutes or less.

B. What is the probability that the arrival time between customers will be between 3 and 7 minutes?

P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3)

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

P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034

P(X \leq 3) = 1 - e^{-0.1*3} = 0.2592

P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3) = 0.5034 - 0.2592 = 0.2442

24.42% probability that the arrival time between customers will be between 3 and 7 minutes

3 0
3 years ago
Am i correct? will mark brainliest
lana [24]

Answer:

no, its 11 for the first one and 45 for the second

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
What is the measure of 2?
Fiesta28 [93]

Answer:

Value of x:

{ \tt{(7x + 1) \degree + (18x + 4) \degree = 180 \degree}} \\  { \tt{25x + 5 = 180}} \\ { \tt{25x = 175}} \\ x = 7

Finding m‹2 :

{ \tt{m \angle2 = (7x + 1) \degree}} \\ { \tt{m \angle2 = (7 \times 7) + 1}} \\ { \bf{m \angle2 = 50 \degree}}

8 0
3 years ago
Read 2 more answers
What is k+3 3/4 = 5 2/3 - 1 1/3
zhenek [66]
K+3 3/4=5 2/3-1 1/3
k+3 3/4=4 1/3
lets find the lcm first then multiply both sides by it but first change it to improper fraction
LCM is  12

[k+15/4]=[13/3]12
12k+45=52
12k=7
k=7/12
4 0
2 years ago
Diana earns $9.95 per hour
Sav [38]

Answer:

m = $9.00 * h.

Step-by-step explanation:

hours: 4, 5, 6, 7,

money: 34, 42.5, 51, 59.5,

5 0
2 years ago
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