Can someone help me with this? Its fairly easy but i genuinely dont remember

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes

andre [41]

Answer:

0.7788 = 77.88% probability that more than three customers arrive in 10 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:

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

In this question, we have that:

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes, and we have three customers, which means that $m = 3*4 = 12, \mu = \frac{1}{12} = 0.0833$

(a) What is the probability that more than three customers arrive in 10 minutes

This is P(X > 3). So

$P(X > 3) = e^{-0.0833*3} = 0.7788$

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

6 0

3 years ago

Is pi/pi irrational

dedylja [7]

Answer:

No, $\frac{\pi}{\pi}$ is 1 which can be written as $\frac{1}{1}$ . The definition of rationals is any number that can be written as a ratio of an integer to an integer where the bottom integer is not 0.

Step-by-step explanation:

$\frac{\pi}{\pi}=1$ since $1(\pi)=\pi$ .

Rational numbers included anything that can be written as a fraction where the top and bottom are integers (bottom integer is not 0).

1 can be written many different ways. It can be written as $\frac{1}{1}$ .

Both the numerator and the denominator of the rewrite of one that I did are integers.

The integers include the following numbers:

{...,-4,-3,-2,-1,0,1,2,3,4,...}.

The integers are the whole numbers and the opposite of the whole numbers.

The whole numbers are {0,1,2,3,4,...}.

The opposite of the whole whole numbers are {...,-4,-3,-2,-1,0}.

3 0

4 years ago

Help me out, please-

olga_2 [115]

unfortunately i cannot

4 0

3 years ago

A box contain 9 novels, 7 biographies, and 5 reference books. Alyssa randomly chooses a book, then she randomly chooses another

Tanzania [10]

$first\ book:\\9\ novels+7\ biographies+5\ reference=21\ all\ books\\probability:\\P_1("chooses\ biographie")= \frac{7}{21} = \frac{1}{3} \\\\second\ book:\\9\ novels+6\ biographies+5\ reference=20\ all\ books\\probability:\\P_2("chooses\ biographie")= \frac{6}{20} = \frac{3}{10}\\\\the\ probablity\ that\ Alyssa\ chooses\ two\ biographies:\\P("two\ biographies")=P_1\cdot P_2= \frac{1}{3}\cdot \frac{3}{10} = \frac{1}{10} =0.1\\\\Ans.\ Probability\ is\ 0.1$

5 0

3 years ago

Rewrite without parentheses and simplify (v-7)^2

Zina [86]

Your answer correct good night

8 0

3 years ago