Mathematics, 21.09.2019 09:10 jasminecoronetti44

Acappuccino vending machine is designed to dispense an average of ? oz per cup. if the ounces per fill are normally distributed, with a standard deviation of 0.4 oz, what value should ? be set at so 6 oz cups will overflow only 2% of the time? 6.82 oz 5.18 oz 5.60 oz 6.00 oz

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Overflow 2% of the time means that the upper tail has an area of 2%, or the lower tail has an area of 100-2=98%.
From tables, P(X<Z)=0.98 => Z=2.0537
We want the maximum fill be 6 oz 98% of the time, or

Mean+Z*(standard deviation)=6 oz
mean = 6oz -2.0537*0.4=5.18 oz

Answer from: nett4386

5.18oz.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$X = 6, \sigma = 0.4$

Overflow only 2% of the time?

Value of $\mu$ when Z has a pvalue of 1-0.02 = 0.98. So X when Z = 2.055.

$Z = \frac{6 - \mu}{\sigma}$

$2.055 = \frac{6 - \mu}{0.4}$

$6 - \mu = 2.055*0.4$

$\mu = 5.18$

So the correct answer is:

5.18oz.

Answer from: Quest

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

$\newline{\text{the rate of change is change per unit time}}$ $\newline{\text{for (x,y), rate of change is }\frac{y_2-y_1}{x_2-x_1} \text{ or change in y divided by change in x}}$ $\newline{\text{for function 1, the cost goes up by 75-45=30 each time every hour}}$ $\newline{\text{that means that the slope of function 1 is 30 per hour}}$ $\newline{\text{for the 2nd function, 40 is added every hour. therefor, the slope is 40 per hour}}$ $\bigskip\newline{\text{since 40 per hour> 30 per hour, function 2 has a greater rate of change than function 1}}$ $\bigskip\newline{\text{the y intercept is the y value when x is 0}}$ $\newline{\text{for function 1, the y value when x is 0 is 45}}$ $\newline{\text{for function 2, the y value when x is 0 (or the flat rate) is 50}}$ $\newline{\text{since 50> 45, function 2 has a greater y intercept than funciton 1}}$ $\bigskip\bigskip\newline{\text{the answers are: }}$ $\newline{\text{ function 2 has a greater rate of change than function 1}}$ $\newline{\text{function 2 has a greater y-intercept than function 1.}}$

Answer from: Quest

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

$y\propto x$

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

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