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2 years ago

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The service time distribution describes the probability P that the service time of the customer will be no more than T hours. If

m is the mean number of customers serviced in an hour, then P=1-e^mt

1 answer:

Molodets [167]2 years ago

7 0

Answer: option d.

Step-by-step explanation:

You have the following formul given in the problem:

$p=1-e^{-mt}$

You know that:

The number of customers serviced in an hour by the technical support representative is 6 costumbers, therefore:

$m=6$

As the problem asked for the probability that a costumber will be on hold less than 30 minutes, we know that:

$t=0.5$

Substitute the values above into the formula.

Then, you obtain:

$p=1-e^{-(6)(0.5)}=0.95$ or 95%

You might be interested in

A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchas

Nataly_w [17]

Answer:

The p value obtained and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidenc to reject the null hypothesis, and we can said that at 5% of significance the proportion of new laptop's with fully charge for the new model is significantly higher compared to the old model.

Step-by-step explanation:

1) Data given and notation n

n=100 represent the random sample taken

X=96 represent the laptop's arrived with fully charged batteries.

$\hat p=\frac{96}{100}=0.96$ estimated proportion of laptop's arrived with fully charged batteries.

$p_o=0.85$ is the value that we want to test

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the new model’s rate is at least as high as the previous model.:

Null hypothesis: $p \leq 0.85$

Alternative hypothesis: $p > 0.85$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.96 -0.85}{\sqrt{\frac{0.85(1-0.85)}{100}}}=3.08$

4) Statistical decision

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level is not provided, but we can assume $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one side test the p value would be:

$p_v =P(z>3.08)=0.0010$

So based on the p value obtained and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidenc to reject the null hypothesis, and we can said that at 5% of significance the proportion of new laptop's with fully charge for the new model is significantly higher compared to the old model.

4 0

2 years ago

At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the numbe

Ilya [14]

Answer:

C. The mean daily salary is greater than $350 per day

Step-by-step explanation:

The computation is shown below:

Y = a + bX

where,

Y = money made by a random selected

a = $150

b = $50

X = number of loan

Now

E(x) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)

= 3.94

Now

E(y) = $150 + ($50 × 3.94)

= $347

hence, the option C is not correct

4 0

1 year ago

Read 2 more answers

Four grey polygons join together as shown in the diagram. I’ve calculated angle a but I don’t know angle b. Angle a is 108

mr Goodwill [35]

Answer:

Part 1) $a=108^o$

Part 2) $b=24^o$

Step-by-step explanation:

Part 1) Find the measure of angle a

we know that

The formula to calculate the measure of the interior angle of a regular polygon is equal to

$\frac{180^o(n-2)}{n}$

where

n is the number of sides of the regular polygon

For the regular pentagon in the figure

n=5

substitute in the formula

$a=\frac{180^o(5-2)}{5}$

$a=\frac{180^o(3)}{5}$

$a=108^o$

Part 2) Find the measure of angle b

Remember that a regular polygon has equal sides and equal interior angles

so

In the figure , the length of the side of the two smaller equilateral triangles is equal to the length of the side of the regular pentagon

therefore

The triangle in white of the figure is an isosceles triangle

The measure of the vertex angle of the isosceles triangle is equal to

$360^o-(108^o+60^o+60^o)=132^o$

Remember that

The sum of the interior angles of triangle must be equal to 180 degrees

so

$2b+132^o=180^o$

solve for b

$2b=180^o-132^o$

$2b=48^o$

$b=24^o$

7 0

2 years ago

Landon babysits and works part time at tge water park over the summer. onw week, he babysat for 3 hours and worked at the water

Tems11 [23]

B = hourly rate for babysitting and w = hourly rate for working at water park

3b + 10w = 109...multiply by -8
8b + 12w = 177...multiply by 3
----------------------
-24b - 80w = - 872 (result of multiplying by -8)
24b + 36w = 531 (result of multiplying by 3)
---------------------add
- 44w = - 341
w = -341/-44
w = 7.75 <=== hourly rate for working at water park

3b + 10w = 109
3b + 10(7.75) = 109
3b + 77.50 = 109
3b = 109 - 77.50
3b = 31.50
b = 31.50/3
b = 10.50 <== hourly rate for babysitting

8 0

2 years ago

Read 2 more answers

mars, inc. claims that 20% of its m&m plain candies are orange. a sample of 100 such candies is randomly selected. find t

elena-14-01-66 [18.8K]

The probability p of an orangecandy is 0.2. The sample size = 100.
The mean is given by:
$n\times p=100\times0.2=20$
The standard deviation is given by:
$\sqrt{npq} = \sqrt{100\times0.2\times(1-0.2)} =4$
The answers are: Mean = 20. Standard deviation = 4.

4 0

2 years ago

Read 2 more answers