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alukav5142 [94]
3 years ago
11

The tip percentage at a restaurant has a mean value of 18% and a standard deviation of 6%.

Mathematics
1 answer:
irakobra [83]3 years ago
8 0

Answer:

a. 0.8366

b. No

Step-by-step explanation:

We will use the central limit theorem which can be applied to a random sample from any distribution as long as the mean and the variance are both finite and the sample size is large (the sample size n should be greater than 30). Here we have that the tip percentage at the restaurant has a mean value of 18% and a standard deviation of 6%, then because of the central limit theorem, we know that the sample mean tip percentage is approximately normally distributed with mean 18% and standard deviation 6/\sqrt{40}%=0.9487%.

a. The z-score related to 16% is given by (16-18)/0.9487 = -2.1081 and the z-score related to 19% is given by (19-18)/0.9487 = 1.0541. We are looking for P(16 < \bar{X} < 19) = P(-2.1081 < Z < 1.0541) = P(Z < 1.0541)- P(Z < -2.1081) = 0.8540 - 0.0175 = 0.8366

b. If the sample size had been 15 rather than 40, then, the probability requested in part (a) could not be calculated from the given information, this because the central limit theorem only applies when the sample size is large, for example n > 30.

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Answer:

area = 24 yd²

Step-by-step explanation:

convert the dimensions into yards using the conversion

1 yard = 3 feet

24 feet = \frac{24}{3} = 8 yards

9 feet = \frac{9}{3} = 3 yards

area = length × width = 8 × 3 = 24 yd²


5 0
3 years ago
A store charges $2.10 for a medium bag of fruit slices. Assuming that the rate stays the same, how much should the store charge
melomori [17]
Hey there,

Your question states: <span>A store charges $2.10 for a medium bag of fruit slices. Assuming that the rate stays the same, how much should the store charge for a large bag of the slices?

So sense this is a medium bad of fruit slices, we would divide 2.10 by 2.

Your answer would be 1.5 Now, all we do is we add 2.10+1.5 and we get 3.15. The reason would be because sense we now know the price of the size of it being small, we just add that size on top of the medium size to get 3.15.

Hope this helps.
~Jurgen</span>
6 0
3 years ago
Read 2 more answers
An image of a parabolic lens is projected onto a graph. The y-intercept of the graph is (0, 90), and the zeros are 5 and 9. Whic
seraphim [82]
Given:

y-intercept of the graph: (0, 90)
zeros: 5 and 9

The equation that models the function based on the zeros given, is either

y = 90 (x-5) (x-9)
or
y= 2(x-5)(x-9)

try solving for the y-intercept of each function, 

y = 90 (0-5) (0-9)
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(0, 4050)

y = 2(0-5) (0-9)
y = 90
(0, 90)

therefore, the equation that models the function is y = 2(x-5)(x-9)

8 0
3 years ago
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The table shows the price for different numbers of board games:
zlopas [31]

Answer:

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

  = 7/2

  = 3.5

For the point (4, 14)

k = y/x

   = 14 / 4

   = 7/2

    = 3.5

For the point (5, 17.50)

k  = y/x

   = 17.5 / 5

   = 3.5

For the point (9, 31.50)

k  = y/x

   = 31.50 / 9

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From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

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The price of 4 board game

y = 3.5 (4)

  = 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

6 0
2 years ago
160,000,000 in scientific notation and 58,413,000,000 please help me guys!!!
elixir [45]

160000000 =

move the decimal so only one number is to the left

we need to move it 8 times

1.60000000 *10^8

1.6*10^8

58413000000

move the decimal so only one number is to the left

5.8413000000 * 10^10

5.8413*10^10

3 0
3 years ago
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