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saveliy_v [14]
2 years ago
13

Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What

is the probability that the call center will get between 4,800 and 5,000 calls in a day
Mathematics
1 answer:
lakkis [162]2 years ago
4 0

Answer:

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 5,500 and standard deviation 1,000.

This means that \mu = 5500, \sigma = 1000

What is the probability that the call center will get between 4,800 and 5,000 calls in a day?

This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So

X = 5000

Z = \frac{X - \mu}{\sigma}

Z = \frac{5000 - 5500}{1000}

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

X = 4800

Z = \frac{X - \mu}{\sigma}

Z = \frac{4800 - 5500}{1000}

Z = -0.7

Z = -0.7 has a p-value of 0.2420.

0.3085 - 0.2420 = 0.0665

0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.

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sergey [27]
Sec θ = 3
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4 0
3 years ago
A student says that if 5x2 = 20, then x must be
lutik1710 [3]

Answer:

I agree with the student's answer. "x" cannot be -2 because then it would make -20 which is not equal to 20:

5(-2)(2) = ?

-10 x 2 = ?

? = -20

-20 ≠ 20

Step-by-step explanation:

Justificaiton:

5(x)(2) = 20

10(x) = 20

10/10(x) = 20/10

x = 2

Second Justification:

5(x)(2) = 20

5/5(x)(2) = 20/5

2x = 4

2x/2 = 4/2

x = 2

4 0
2 years ago
John paid $222 for four hours of skiing and two hours boating. He paid $213 for two hours skiing and three hours boating. What i
Inga [223]

Answer:

Skiing costs $30 per hour and Boating costs $51 per hour.

Step-by-step explanation:

Let cost per hour of skiing be x and cost per hour of boating be y. Let's dissect the problem into 2 simultaneous equations.

<em><u>"John paid $222 for four hours of skiing and two hours boating":</u></em>

4x+2y=222

<em><u>"He paid $213 for two hours skiing and three hours boating":</u></em>

2x+3y=213

<em>Now, if we solve for x in the 2nd equation and plug it in the 1st equation, we will have the value for y</em>. Work shown below.

2x+3y=213\\2x=213-3y\\x=\frac{213-3y}{2}\\Equation 1: 4x+2y=222\\Substituting :\\4(\frac{213-3y}{2})+2y=222\\2(213-3y)+2y=222\\426-6y+2y=222\\426-222=6y-2y\\204=4y\\y=\frac{204}{4}=51

Hence, y = 51

<em>Now, substituting this y value into the 1st equation and solving for x will give us the value of x.</em>

First Equation: 4x+2y=222\\4x+2(51)=222\\4x+102=222\\4x=222-102\\4x=120\\x=\frac{120}{4}=30

Hence, skiing costs $30 per hour and boating costs $51 per hour.

4 0
3 years ago
PLEASE HELP ME WITH THESE QUESTIONS!!
Varvara68 [4.7K]

Answer:

3. [1, −2]

2. [−3, 3]

1. [−7, 10]

Step-by-step explanation:

3.

{7⁄2x - ½y = 9⁄2

{3x - y = 5

-6⁄7[7⁄2x - ½y = 9⁄2]

{−3x + 3⁄7y = −3 6⁄7 >> New Equation

{3x - y = 5

_________________

-4⁄7y = 1 1⁄7

-2 = y [Plug this back into both equations above to get the x-coordinate of 1]; 1 = x

__________________________________________________________

2.

{−3x + 9y = 36

{4x + 12y = 24

¾[4x + 12y = 24]

{−3x + 9y = 36

{3x + 9y = 18

______________

18y = 54

___ ___

18 18

y = 3 [Plug this back into both equations above to get the x-coordinate of −3]; −3 = x

__________________________________________________________

1.

{4x − y = −38

{x + y = 3

_____________

5x = -35

___ ____

5 5

x = -7 [Plug this back into both equations above to get the y-coordinate of 10]; 10 = y

I am joyous to assist you anytime.

3 0
3 years ago
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Answer:what it is

Step-by-step explanation:

6 0
3 years ago
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