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tresset_1 [31]
3 years ago
7

7) In Problem 6 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts

in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces. a) Find the expected amount of cereal left in the box. b) What’s the standard deviation? c) If the weight of the remaining cereal can be described by a Normal model, what’s the probability that the box still contains more than 13 ounces?
Mathematics
1 answer:
olga_2 [115]3 years ago
3 0

Question:

The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.

Answer:

a) The expected amount of cereal left in the box is 12.2 ounces

b) The standard deviation  \sigma_{x+y+z}, is 0.5099

c) In a Normal model, the probability that the box still contains more than 13 ounces is P(Z-(X+Y) > 13) = 5.821 %.

Step-by-step explanation:

Let X represent the amount of cereal that can be poured into a small bowl and Y represent the amount of cereal that can be poured into a large bowl and Z represent the amount of cereal that the manufacturer puts in the box, then the expected amount of cereal left in the box is given by

Z - (X + Y)

(a) The expected amount of cereal left in the box is given as

P(Z - (X + Y)) = μ = μ_Z - μ_X - μ_Y = 16.2 - 1.5 - 2.5 = 12.2 ounces

The expected amount of cereal left in the box = 12.2 ounces

b) The standard deviation is given by  the root of the sum of the variance

That is

\sigma_{x+y+z} ^2 = \sigma_x^2 + \sigma_y^2 +\sigma_z^2 and

\sqrt{\sigma_{x+y+z} ^2}  = \sqrt{\sigma_x^2 + \sigma_y^2 +\sigma_z^2} =\sqrt{0.1^2+0.4^2+0.3^2} = 0.5099

The standard deviation,  \sigma_{x+y+z}, = 0.5099

c) The probability that the box still contains more than 13 ounces is given by

P(Z-(X+Y) > 13)

Where z-score is  

z=\frac{x-\mu}{\sigma} = \frac{13-12.2}{0.5099}=  1.5689 ≈ 1.57

From the z-score table P(Z = 1.57) = 0.94179

Therefore the probability of the box containing ≤ 13 is 0.94179, that is

P(Z-(X+Y) ≤ 13) = 0.94179 and

P(Z-(X+Y) > 13) = 1 - 0.94179 = 0.05821 = 5.821 %.

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Solve the system below by substitution. Give your answer as an ordered pair.
bearhunter [10]
Work:
2x+5(6x+23)=-13
2x+30x+115=-13
32x=-128
x=-4

y=6(-4)+23
y=-24+23
y=-1

The answer is (-4,-1)

Hopefully this helps!
6 0
3 years ago
The total number of people at a football game was 5600. Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.
rewona [7]

Answer:

1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

x+y=5600...(1)

y=5600-x...(1)    

We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be 40x and cost of y end-zone tickets would be 20y.

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

40x+20y=134000...(2)

Upon substituting equation (1) in equation (2), we will get:

40x+20(5600-x)=134000

40x+112000-20x=134000

20x+112000=134000

20x+112000-112000=134000-112000

20x=22000

\frac{20x}{20}=\frac{22000}{20}

x=1100

Therefore, 1100 field side tickets were sold.

Upon substituting x=1100 in equation (1), we will get:

y=5600-1100

y=4500

Therefore, 4500 end-zone tickets were sold.

3 0
3 years ago
Peter works as a delivery person for a bike shipping company. The graph shows a linear model for his delivery times on different
aev [14]

Answer/Step-by-step explanation:

✍️The equation of the line in point-slope form:

The equation is given as y - b = m(x - a), where,

(a, b) = a point on the line.

slope (m) = \frac{y_2 - y_1}{x_2 - x_1}

Let's find the slope (m) of the line, housing (3, 21) and (6, 12):

slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 21}{6 - 3} = \frac{-9}{3} = -3

Substitute a = 3 and b = 21, m = -3 into y - b = m(x - a).

Thus, the point-slope equation would be:

✅y - 21 = -3(x - 3)

✍️The equation of the line in slope-intercept form:

Rewrite y - 21 = -3(x - 3), so that y is made the subject of the formula.

y - 21 = -3x + 9

Add 21 to both sides

y = -3x + 9 + 21

y = -3x + 30

✅The slope-intercept equation of the line is y = -3x + 30

Where,

-3 = how much did his delivery time decrease per day (slope)

30 = how long it initially took Peter to deliver his packages (y-intercept)

5 0
3 years ago
Find cp if so =rs 800 and loss% = 10%​
rjkz [21]

Step-by-step explanation:

Sp = rs 800

loss = 10%

Cp = ?

we know that,

cp= sp×100÷ 100-L%

= 800×100÷100-10

= 80000÷90

= 888.89#

3 0
3 years ago
Read 2 more answers
What are the square roots of 36100?
sleet_krkn [62]

\huge\text{Hey there!}

\large\textsf{What are \bf the square roots of 36,100?}

\mathsf{\sqrt{36,100}=190\times190 = \bold{190}^2}

\mathsf{190^2=36,100}

\mathsf{(- 190)^2=36,100}

\mathsf{190\times190=36,100}

\mathsf{\sqrt{36,100}=\bf 190}

\mathsf{-\sqrt{36,100}=\bf -190}

\boxed{\boxed{\large\text{Answer: \huge \bf -190 and 190}}}\huge\checkmark

\text{Good luck on your assignment and enjoy your day!}

~\frak{Amphitrite1040:)}

8 0
3 years ago
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