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defon
3 years ago
8

The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served w

as 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays.
Mathematics
1 answer:
Oliga [24]3 years ago
5 0

Answer:

(121.576 ; 273.424)

Step-by-step explanation:

Given the data:

175, 125, 180, 220, 240, 245

We can calculate the mean and standard deviation

Mean = Σx/ n = 1185 / 6 = 197.5

Standard deviation = 46.125 (calculator)

The confidence interval :

Mean ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Tcritical at 99%, df = n - 1 ; 6 - 1 = 5

Tcritical = 4.032

Margin of Error = 4.032 * 46.125/√6

Margin of error = 75.924

Confidence interval :

197.5 ± 75.924

Lower boundary = 197.5 - 75.924 = 121.576

Upper boundary = 197.5 + 75.924 = 273.424

(121.576 ; 273.424)

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g A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estim
kipiarov [429]

Answer:

a) n= 1045 computers

b) n= 442 computers

c) A. ​Yes, using the additional survey information from part​ (b) dramatically reduces the sample size.

Step-by-step explanation:

Hello!

The variable of interest is

X: Number of computers that use the new operating system.

You need to find the best sample size to take so that the proportion of computers that use the new operating system can be estimated with a 99% CI and a margin of error no greater than 4%.

The confidence interval for the population proportion is:

p' ± Z_{1-\alpha /2} * \sqrt{\frac{p'(1-p')}{n} }

Z_{1-\alpha /2}= Z_{0.995}= 2.586

a) In this item there is no known value for the sample proportion (p') when something like this happens, you have to assume the "worst-case scenario" that is, that the proportion of success and failure of the trial are the same, i.e. p'=q'=0.5

The margin of error of the interval is:

d= Z_{1-\alpha /2} * \sqrt{\frac{p'(1-p')}{n} }

\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p)}{n} }

(\frac{d}{Z_{1-\alpha /2}})^2 = \frac{p'(1-p')}{n}

n * (\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')

n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2

n=[0.5(1-0.5)]*(\frac{2.586}{0.04} )^2= 1044.9056

n= 1045 computers

b) This time there is a known value for the sample proportion: p'= 0.88, using the same confidence level and required margin of error:

n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2

n= [0.88*0.12]*(\frac{{2.586}}{0.04})^2= 441.3681

n= 442 computers

c) The additional information in part b affected the required sample size, it was drastically decreased in comparison with the sample size calculated in a).

I hope it helps!

4 0
4 years ago
Which of the following functions is graphed below?
Butoxors [25]

Answer:

Option (B)

Step-by-step explanation:

Given question is not complete; find the complete question in the attachment.

In the graph attached,

Parent function is an absolute value function,

f(x) = |x|

When this graph is shifted 4 units left, rule for the translation will be,

f(x) → f(x + 4)

Therefore, the new function of above translation will be,

g(x) = f(x + 4) = |x + 4|

Now the graph is shifted 2 units down so the translated function will be,

h(x) = g(x) - 2

h(x) = |x + 4| - 2

If we rewrite the function in the form of an equation, graph will be represented by

⇒ y = |x + 4| - 2

Therefore, Option (B) will be the answer.

8 0
3 years ago
Can someone help?
lutik1710 [3]

Answer:

<em>21(a) 8 cm</em>

<em>21(b) 1.6 cm/sec</em>

Step-by-step explanation:

21(a)

21 cm = 13 cm = 8 cm

21(b)

Increase in depth from 6 sec to 11 sec: 8 cm

Time from 6 sec to 11 sec: 11 sec - 6 sec = 5 sec

Rate = (8 cm)/(5 sec) = 1.6 cm/sec

3 0
4 years ago
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GREYUIT [131]

Answer:

How to calculate and derive the formula for the Chord Length of a circle. The formula for the chord length is: 2rsin(theta/2) where r is the radius of the circle and theta is the angle from the centre of the circle to the two points of the chord.

8 0
3 years ago
The ratio of j to 40 is 1 to 2. What is the value of j?<br> A) 1<br> B) 10<br> C) 20<br> D) 80
GrogVix [38]

Answer:

c

Step-by-step explanation:

5 0
4 years ago
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