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meriva
3 years ago
6

A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation

of 3 ounces. What is the probability of filling a cup between 22 and 29 ounces? Round your answer to four decimal places.
Mathematics
1 answer:
postnew [5]3 years ago
6 0

Answer: P(22 ≤ x ≤ 29) = 0.703

Step-by-step explanation:

Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = output of the machine in ounces per cup.

µ = mean output

σ = standard deviation

From the information given,

µ = 27

σ = 3

The probability of filling a cup between 22 and 29 ounces is expressed as

P(22 ≤ x ≤ 29)

For x = 22,

z = (22 - 27)/3 = - 1.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.047

For x = 29,

z = (29 - 27)/3 = 0.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.75

Therefore,

P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703

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dmitriy555 [2]

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Step-by-step explanation:

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Rami bought a house on 1st January 2015. In2015 the house increased in value by 15%. In 2016 the house decreased in value by 8%.
shepuryov [24]

Answer:

The value of the house on 1st January 2015 was of $650,000.

Step-by-step explanation:

Decimal multipliers:

For a increase of a%, the decimal multiplier is given by \frac{100+a}{100}

For a decrease of a%, the decimal multiplier is given by \frac{100-a}{100}

Rami bought a house on 1st January 2015.

For a value of x.

In 2015 the house increased in value by 15%.

This means that x is multiplied by \frac{100+15}{100} = \frac{115}{100} = 1.15

In 2016 the house decreased in value by 8%.

This means that 1.15 times x is multiplied by \frac{100-8}{100} = \frac{92}{100} = 0.92

On 1st January 2017 the value of the house was $687700.

The value of these multiplications is 687700.

What was the value of the house on 1st January 2015?

This is x, so:

x*1.15*0.92 = 687700

x = \frac{687700}{1.15*0.92}

x = 650000

The value of the house on 1st January 2015 was of $650,000.

7 0
3 years ago
Jack works after school. Each day he is paid a set amount, plus an hourly wage. Look at the table. Choose the linear function f
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Answer:

The correct linear equation is;

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Step-by-step explanation:

To choose the correct linear function, we just need to take a specific point, then substitute in each of the equations given to get the one right

The correct one will be the one in which when the x-value is substituted, we will get the y-value

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Let us begin testing;

A. f(x) = 10x + 8

f(1) = 10(1) + 8 = 10 + 8 = 18

Let us use another point to test this

The second point is (1.5,23)

f(1.5) = 10(1.5) + 8

= 15 + 8 = 23

7 0
3 years ago
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