A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. if the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time?
Answers
z=(x-μ)/σ
the z-score associated with 0.5% is 0
thus
0=
(8-μ)/0.4=0
solving for x we get:
μ=9
Answer: μ=9
Final answer:
The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.
Explanation:
The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.
Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.
Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.
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The value of the expression 588 ÷ 6 will be 98. Then the number of digits is 2.
What is Algebra?
Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and correctly.
The numbers are given below.
588 and 6
Then the division between the numbers 588 and 6 will be given by putting a division sign between them. Then we have
⇒ 588 ÷ 6
⇒ 588/6
⇒ 98
The value of the expression 588 ÷ 6 will be 98. Then the number of digits is 2.
More about the Algebra link is given below.
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Answers
Answer:
Answer:
true
false
true
Step-by-step explanation:
B. 0 ÷ 28 = 0
C. 28 – 0 = 0
D. 28 ÷ 0 = 0
Answers
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28 + 0 = 28 not 0.
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Answers
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Hope this helps :)
Answers
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both multiply by 3
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both divide by 2
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4. Subtract the expressions (2w + 3) - (w + 3)
5. What is the result when 2a - 5 is subtracted from 3a + 3?
Answers
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4. w