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Black_prince [1.1K]
2 years ago
10

Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hou

rs. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 51 from the available frame. The sample mean and sample standard deviations were 48.5 and 7.5 hours, respectively. Construct a 99% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week
Mathematics
1 answer:
Reil [10]2 years ago
7 0

Answer:  (45.79, 51.21)

Step-by-step explanation:

Given : Significance level : \alpha: 1-0.99=0.01

Sample size : n= 51 , which is a large sample (n>30), so we use z-test.

Critical value: z_{\alpha/2}=2.576

Sample mean : \overline{x}= 48.5\text{ hours}

Standard deviation : \sigma=7.5\text{ hours}

The confidence interval for population means is given by :-

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

i.e. 48.5\pm(2.576)\dfrac{7.5}{\sqrt{51}}

i.e.48.5\pm2.70534112234\\\\\approx48.5\pm2.71\\\\=(48.5-2.71, 48.5+2.71)=(45.79, 51.21)

Hence, 99% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week =  (45.79, 51.21)

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Answer:

  65.3 cm

Step-by-step explanation:

The law of sines can be used for this.

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The length of g is about 65.3 cm.

6 0
2 years ago
A........ divides a two - dimensional shape into two congruent shapes​
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A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)

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The area of the rectangle is 64.8 square centimeters. What is the perimeter of the rectangle? One group of ten tenths and one gr
9966 [12]

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(b) 100

Step-by-step explanation:

Solving (a):

Given

Shape: Rectangle

Area = 64.8

Required

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Area is calculated as:

Area = L * W

Where

L = Length and W = Width

Substitute 64.8 for Area

64.8 = L * W

Make L the subject:

L = \frac{64.8}{W}

Perimeter is calculated as:

P = 2 * (L + W)

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P = \frac{129.6}{W} + 2W

To solve further, we take the derivative of P and set it to 0, afterwards.

dP = -\frac{129.6}{W^2} + 2

Set to 0

0 = -\frac{129.6}{W^2} + 2

Collect Like Terms

\frac{129.6}{W^2} = 2

Cross Multiply:

2W^2= 129.6

Divide through by 2

W^2 = 64.8

Take square roots

W = \sqrt{64.8

W = 8.05

Recall that:

L = \frac{64.8}{W}

So:

L= \frac{64.8}{8.05}\\

L= 8.05

The perimeter is:

Perimeter = 2 * (8.05 + 8.05)

Perimeter = 2 * (16.10)

Perimeter = 32.2\ cm

Solving (b):

Given

((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)

Required

Solve

Tenths = \frac{1}{10}

So, the expression becomes:

((1 Group of 10 * \frac{1}{10}) and (1 group of 8 * \frac{1}{10}))/(6 groups of 3 * \frac{1}{10})

This gives:

((1 Group of \frac{10}{10}) and (1 group of \frac{8}{10}))/(6 groups of \frac{3}{10})

Group means product, so the expression becomes:

\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}

And, as used here means addition

\frac{(1 * \frac{10}{10} +  1 * \frac{8}{10})}{6 * \frac{3}{10}}

Simplify:

\frac{(1 * 1 +  1 * 0.80)}{6 *0.30}

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7 0
2 years ago
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Answer:

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