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frez [133]
3 years ago
6

The distribution of the weights of a sample of 140 cargo containers is symmetric and bell-shaped, with a mean of 500 pounds and

a standard deviation of 20 pounds. What percentage of the cargo containers will weigh between 460 pounds and 540 pounds?
a. 95%
b. Can't tell-there is not enough information
c. 67%
d. 99%
Mathematics
1 answer:
I am Lyosha [343]3 years ago
6 0

Answer:

a. 95%

Step-by-step explanation:

We solve this question, using z score formula.

Z score formula = (x - μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

n is number of samples

For z1, where x1 = 460, μ = 500, σ = 20, n = 140

z score formula = (460 - 500)/ 20

= -40/20

= -2

We find the probability of the z score using the z score table.

P(x = 460) = P(z = -2)

= 0.02275

For z2, where x2 = 540, μ = 500, σ = 20

z score formula = (540 - 500)/20

= 40/20

= 2

We find the probability of the z score using the z score table.

P(x = 540) = P(z = 2)

= 0.97725

The probability that the cargo containers will weigh between 460 pounds and 540 pounds is calculated as:

= 460 < x < 540

= P(z = 2) - P(z = -2)

= 0.97725 - 0.02275

= 0.9545

Converting to percentage

0.9545 × 100

= 95.45%

Therefore,the percentage of the cargo containers will weigh between 460 pounds and 540 pounds is 95%

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a set of average city temperatures in december are normally distributed with a mean of 16.3°C and a standard deviation of 2°C. w
koban [17]

Answer:

19.74% of temperatures are between 12.9°C and 14.9°C

Step-by-step explanation:

Problems of normally distributed samples are 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 question, we have that:

\mu = 16.3, \sigma = 2

What proportion of temperatures are between 12.9°C and 14.9°C?

This is the pvalue of Z when X = 14.9 subtracted by the pvalue of Z when X = 12.9.

X = 14.9

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

Z = \frac{14.9 - 16.3}{2}

Z = -0.7

Z = -0.7 has a pvalue of 0.2420

X = 12.9

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

Z = \frac{12.9 - 16.3}{2}

Z = -1.7

Z = -1.7 has a pvalue of 0.0446

0.2420 - 0.0446 = 0.1974

19.74% of temperatures are between 12.9°C and 14.9°C

3 0
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LenaWriter [7]
Instanteous speed is what it is

4 0
2 years ago
2/3 years = how many months?
Dovator [93]

Answer:

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Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A cylinder is placed within a cube. The diameter of the cylinder is equal to the length of each side of the cube. What is the vo
pochemuha

The volume of a shape is the amount of space in it.

<em>The volume outside the cylinder, but inside the cube is 214.6 cubic inches</em>

The given parameter is:

l = 10 ---- length of the cube

So, the volume of the cube is:

V_1 = l^3

V_1 = 10^3

V_1 = 1000

The volume of the cylinder is:

V_2 = \pi r^2h

The diameter (d) of the cylinder equals the length of the cube.

This means that:

d = l

d = 10

Divide by 2 to calculate the radius of the cylinder

r = \frac{10}{2}

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Also, the height of the cube is::

h =l

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So, we have:

V_2 = \pi r^2h

V_2 = \pi \times 5^2 \times 10

V_2 = \pi \times 25 \times 10

V_2 = \pi \times 250

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V = 1000 - 785.4

V = 214.6

Hence, the volume outside the cylinder is 214.6 cubic inches

Read more about volumes at:

brainly.com/question/15861918

5 0
2 years ago
Please help and stop with the links!
ira [324]
It C)
This is because the sum of the two smaller sides in a triangle has to be larger than the bigger sides. 10+12=22.
22 is smaller than 24 which is the third side this no triangle is formed
5 0
3 years ago
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