Find the value of x when lines w and v are parallel.

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.The ma

Lana71 [14]

Answer:

The advertisement should use 16 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:

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

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.

This means that $m = 3.5, \mu = \frac{1}{3.5} = 0.2857$

What number of minutes should the advertisement use?

The values of x for which:

$P(X > x) = 0.01$

So

$e^{-\mu x} = 0.01$

$e^{-0.2857x} = 0.01$

$\ln{e^{-0.2857x}} = \ln{0.01}$

$-0.2857x = \ln{0.01}$

$x = -\frac{\ln{0.01}}{0.2857}$

$x = 16.12$

Rounding to the nearest number, the advertisement should use 16 minutes.

5 0

3 years ago

Solve for b. Help pls thank u !!!!

Nadusha1986 [10]

Step-by-step explanation:

3b - 3.76 = 1.34

3b = 3.76+ 1.34

3b = 5.1

b= 5.1/3

= 1.7

5 0

3 years ago

To win a particular lottery game, it is necessary to match numbers on 5 balls that are randomly picked from 65 balls numbered 1-

emmainna [20.7K]

Answer: $5.34*10^{-5}$

Step-by-step explanation:

given data:

number of balls = 65.

special black ball that is picked from 10 other balls = numbered 0-9.

Solution:

probability that a single lottery ticket will match 2 balls and the special black ball.

$= 65C2*9C1\\\\= 18720\\\\=\frac{1}{18720} \\\\= 5.34*10^{-5}$

5 0

3 years ago

Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636, the central limit theorem appl

lakkis [162]

Answer:

a) $\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)$

$\mu_{\bar X}=100$ $\sigma^2_{\bar X}=1$

b) $P(\bar X >101)=1-P(\bar X$

c) $P(\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$