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Juli2301 [7.4K]
3 years ago
12

You are contacted by a phone-in technical support business that is interested in some information about the amount of time their

customers spend on hold. You find out that on average, each caller spends 11 minutes on hold with a standard deviation of 1.16 minutes. If you were to take a random sample of 62 callers, you would expect 79% of the time the average hold time would be greater than how many minutes?
Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0

Answer:

The average hold time is 10.47 minutes.

Step-by-step explanation:

Let <em>X</em> = time the customers of a phone-in technical support business spend on hold.

The population mean of the random variable <em>X</em> is, <em>μ</em> = 11 minutes.

The population standard deviation of the random variable <em>X</em> is, <em>σ </em>= 1.16 minutes.

A random sample size, <em>n</em> = 62 callers are selected.

According to the Central limit theorem if large samples (<em>n</em> > 30) are selected from an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> then the sampling distribution of sample mean (\bar x) follows a Normal distribution.

The mean of the sampling distribution of sample mean is:

\mu_{\bar x}=\mu=11

The standard deviation of the sampling distribution of sample mean is:

\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{1.16}{\sqrt{62}}=0.147

It is provided that P(\bar X>a)=0.79.

Compute the value of <em>a</em> as follows:

P(\bar X>a)=0.79\\P(Z>z)=0.79\\1-P(Z

The value of <em>z</em> for the above probability is, <em>z</em> = -0.806.

The value of <em>a</em> is:

z=\frac{a-\mu_{\bar x}}{\sigma_{\bar x}}\\-0.806=\frac{a-11}{0.147}\\a=11-(0.86\times 0.147)\\a=10.87

Thus, the average hold time is 10.47 minutes.

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Step-by-step explanation:

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A rock is thrown upward from a bridge that is 22 feet above a road. The rock reaches its maximum height above the road 0.69 seco
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Answer:

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Explanation:

The<em> hint </em>is that the function f can be written in the form:

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The maximum point, maximum height, of a parabola is its vertex.

And the x-coordinate of the vertex is at the midpoint between the two x-intercepts.

The time when the rock reaches the road is one x-intercept: t = 2.53 seconds: (2.53, 0).

The other x-intercept is sucht that (x + 2.53) / 2 = 0.69

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Thus, the equation is:

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Answer:

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Step-by-step explanation:

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To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)

\displaystyle \frac{3}{2} = \frac{2 \times 3}{2 \times 2} = \frac{6}{4}.

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At this point, the difference between the numerators is now 2. That allows a number (7 in this case) to fit between the bounds. However, \displaystyle \frac{1}{c} = \frac{4}{7} can't be written as finite decimals.

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\displaystyle \frac{4}{2} = \frac{5\times 4}{5 \times 2} = \frac{20}{10}.

It is important to note that some expressions for c can be simplified. For example, \displaystyle \frac{16}{10} = \frac{2 \times 8}{2 \times 5} = \frac{8}{5} because of the common factor 2.

Apparently \displaystyle c = \frac{16}{10} = \frac{8}{5} works. c = 1.6 while \displaystyle \frac{1}{c} = \frac{5}{8} = 0.625.

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