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Masteriza [31]
3 years ago
14

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distribut

ed with a mean of 7.6oz and standard deviation of 0.4oz.
(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.)
(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)
(c) The machine has just been loaded with 848 cups. How many of these do you expect will overflow when served
Mathematics
1 answer:
klemol [59]3 years ago
4 0

Answer:

Step-by-step explanation:

Since the amount of soft drink dispensed into a cup is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = amount in ounce of soft drink dispensed into cup.

µ = mean amount

σ = standard deviation

From the information given,

µ = 7.6oz

σ = 0.4 oz

a) The probability that the machine will overflow an 8-ounce cup is expressed as

P(x > 8) = 1 - P(x ≤ 8)

For x = 8,

z = (8 - 7.6)/0.4 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

P(x ≤ 8) = 1 - 0.84 = 0.16

b) P(x< 8) = 0.84

c) when the machine has just been loaded with 848 cups, the number of cups expected to overflow when served is

0.16 × 848 = 136 cups

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VikaD [51]

It is necessary to imagine the sum of the areas between each z-score and the average.

Given as the ratio of the area under the normal curve between two z-scores, both above average.

The  Z score accurately measures the number of standard deviations above or below the mean of the data points.

The formula for calculating the z-score is

z = (data points – mean) / (standard deviation).

It is also expressed as z = (x-μ) / σ.

  • A positive z-score indicates that the data points are above average.
  • A negative z-score indicates that the data points are below average.
  • A z-score close to 0 means that the data points are close to average.
  • The normal curve is symmetric with respect to the mean and needs to be investigated.

Therefore, to find the percentage of the area under the normal curve between two z-scores, both above the mean, you need to look at the sum of the areas between the z-score and the mean.

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7 0
1 year ago
The weight of a bull clad is 388 kilograms. If it’s weight increases at a rate of 1 2/5 kilograms per day how long it will take
Alex73 [517]

Answer:

It will take  <u><em>80 days</em></u>  for the bull calf to reach a weight of 500 kilograms.

Step-by-step explanation:

Given:

The weight of a bull calf is 388 kilograms.

Now, to find the weight of bull calf of how long it will take to reach a weight of 500 kilograms, if it’s weight increases at a rate of 1 2/5 kilograms per day.

Required weight which to be increased = 500 - 388 = 112 kilograms.

Rate of weight increase = 1\frac{2}{5}=\frac{7}{5}

                                        = 1.4\ kilograms.

Thus, the time required = \frac{required\ weight}{rate\ of\ weight}

                                        = \frac{112}{1.4}

                                        = 80.

<em>The time required   =    80 days</em>.

Therefore, it will take 80 days for the bull calf to reach a weight of 500 kilograms.

5 0
3 years ago
Elevation is a measure of height in relation to sea level. The highest feature on Earth is Mount Everest with an elevation +29,0
Sphinxa [80]

Answer:

Sea\ Level = 0\ ft

The farthest point is the Challenger Deep

Step-by-step explanation:

Given

Highest = +29029ft

Least = -35,797ft

Solving (a): The sea level

Both elevations had signs in front of them.

The sea level is the point at the neutral level, neither positive nor negative.

Hence:

Sea\ Level = 0\ ft

Solving (b): Farthest Point.

The farthest point is the one with the highest magnitude.

Comparing

Highest = +29029ft  to   Least = -35,797ft

-35,797 ft has the highest magnitude.

Hence:

<em>The farthest point is the Challenger Deep</em>

5 0
3 years ago
Eddie took out a 14-year loan for $72,000 at an APR of 4.7%, compounded monthly, while Lee took out a 14-year loan for $92,000 a
marishachu [46]
**Eddie: $72000/(14yr*12mo)=428.6$/mo+428.6$*(4.7%)/100%
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**Lee: $92000/(14yr*12mo)=547.62$/mo+547.62$*(4.7%)/100%
Lee pays 547.62$/mo+25.74$/mo. If he pays off his loan 6 years earlier he would save: $25.74*6yr*12mo=$1853.28

So its A. <span>Lee would save more, since he has $20,000 more in principal.</span>
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