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3 years ago

11

The number of orders received daily by an online vendor of used CDs is normally distributed with mean 270 and standard deviation

16. The company has to hire extra help or pay overtime on those days when the number of orders received is 302 or higher. What percentage of days will the company have to hire extra help or pay overtime?

1 answer:

frez [133]3 years ago

4 0

Answer:

Step-by-step explanation:

Given that the number of orders received daily by an online vendor of used CDs (say X) is normally distributed with mean 270 and standard deviation 16.

X is N(270, 16)

To find percentage of days will the company have to hire extra help or pay overtime, we can find probability using std normal table

X>302 means

$Z>\frac{302-270}{16} =2$

P(Z>2) = 0.25

Thus 25% of days will the company have to hire extra help or pay overtime

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iren2701 [21]

Answer:

I believe the correct answer is Building B

Step-by-step explanation:

Building A is 23.45 per employee and Building B is 25.67 per employee

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3 years ago

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4 years ago

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What is the domain of the function? y=3√x-1

geniusboy [140]

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3 years ago

f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

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:

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

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

If ∠D is a supplementary angle of ∠E and ∠F is a supplementary angle of ∠E, then which of the following statements is true?

Romashka [77]

Answer:

A) ∠D ≅ ∠F

Step-by-step explanation:

<u>Supplementary angles</u> : A pair of angles whose sum is 180° are called supplementary angles

We are given that ∠D is a supplementary angle of ∠E

So, $\angle D+\angle E = 180^{\circ} -----1$

We are also given that ∠F is a supplementary angle of ∠E

So, $\angle F+\angle E = 180^{\circ} ------2$

Find the value of ∠E form 1 and 2

From 1 : $\angle E = 180^{\circ}-\angle D$

From 2 : $\angle E = 180^{\circ}-\angle F$

So, $180^{\circ}-\angle D=180^{\circ}-\angle F$

$\angle D=\angle F$

So, Option A is true

Hence ∠D ≅ ∠F

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3 years ago