Which is greater 20.903 or 2.209

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate

Leviafan [203]

Answer:

Probability of having student's score between 505 and 515 is 0.36

Given that z-scores are rounded to two decimals using Standard Normal Distribution Table

Step-by-step explanation:

As we know from normal distribution: z(x) = (x - Mu)/SD

where x = targeted value; Mu = Mean of Normal Distribution; SD = Standard Deviation of Normal Distribution

Therefore using given data: Mu (Mean) = 510, SD = 10.4 we have z(x) by using z(x) = (x - Mu)/SD as under:

In our case, we have x = 505 & 515

Approach 1 using Standard Normal Distribution Table:

z for x=505: z(505) = (505-510)/10.4 gives us z(505) = -0.48

z for x=515: z(515) = (515-510)/10.4 gives us z(515) = 0.48

Afterwards using Normal Distribution Tables and rounding the values to two decimals we find the probabilities as under:

P(505) using z(505) = 0.32

Similarly we have:

P(515) using z(515) = 0.68

Now we may find the probability of student's score between 505 and 515 using:

P(505 < x < 515) = P(515)-P(505) = 0.68 - 0.32 = 0.36

PS: The standard normal distribution table is being attached for reference.

Approach 2 using Excel or Google Sheets:

P(x) = norm.dist(x,Mean,SD,Commutative)

P(505) = norm.dist(505,510,10.4,1)

P(515) = norm.dist(515,510,10.4,1)

Probability of student's score between 505 and 515= P(515) - P(505) = 0.36

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6 0

3 years ago

Mhanifa please help :( no one has helped me on this yet

VMariaS [17]

Answer:

16)

q / 12 = sin 20
q = 12 sin 20
q = 4.1

p / 12 = cos 20
p = 112 cos 20
p = 11.3

17)

x / 44 = tan 39
x = 44 tan 39
x = 35.6

35.6 / y = sin 39
y = 35.5 / sin 39
y = 56.4

18)

14 / b = sin 57
b = 14 / sin 57
b = 16.7

a / 16.7 = cos 57
a = 16.7 cos 57
a = 9.1

3 0

3 years ago

What is the rational number equivalent to 3.12

jekas [21]

Answer:

3 4/33

Step-by-step explanation:

3 0

3 years ago

Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for reg

Contact [7]

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) Optimal solution: 40.000 units of R and 10.000 of PC = $17.000

c) Slack variables: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) Binding Constaints:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.

3 0

3 years ago

The number of boots that 25 students had in their homes in Florida were recorded below:

Doss [256]

Answer:

A) 8

B) Significantly (increased)

C) Not affected

D) Median

E) Significantly (increased)

F) Not affected

G) Interquartile range

Step-by-step explanation:

A)

When we have a certain set of data, we call "outlier" a value in this set of data that is significantly far from all the other values.

In this problem, we see that we have the following set of data:

0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,4,5,8

We see that all the values between 0 and 5 are relatively close to each other, being only 1 number distant from any other value.

On the other hand, the last value "8" is 3 numbers distant from the other highest value ("5"), so the outliar is 8.

B)

The mean of a certain set of value indicates the "average" value of the dataset. It is given by:

$\bar x = \frac{\sum x_i}{N}$

where

$\sum x_i$ is the sum of all the values in the dataset

N is the number of values in the dataset (in this case, 25)

An outlier usually affects a lot the mean, because it changes the value of the sum $\sum x_i$ by quite a lot.

In fact in this problem, we have

$\sum x_i = 47$

N = 25

So the mean is

$\bar x=\frac{47}{25}=1.88$

Instead, without the outliar "8",

$\sum x_i = 39\\N=24$

And the mean would be

$\bar x=\frac{39}{24}=1.63$

So we see that the outlier increases the mean significantly.

C)

The median of a dataset is the "central value" of the dataset: it means it is the value for which 50% of the values of the dataset are above the median and 50% of the values of the dataset are below the median.

In this problem, we have 25 values in the dataset: so the median is the 13th values of the ordered dataset (because if we take the 13th value, there are 12 data below it, and 12 data above it). The 13th value here is a "2", so the median is 2.

We see also that the outlier does not affect the median.

In fact, if we had a "5" instead of a "8" (so, not an outlier), the median of this dataset would still be a 2.

D)

The center of a distribution is described by two different quantities depending on the conditions:

- If the distribution is symmetrical and has no tails/outliers, then the mean value is a good value that can be used to describe the center of the distribution.

- On the other hand, if the distribution is not very symmetrical and has tails/outliers, the median is a better estimator of the center of the distribution, because the mean is very affected by the presence of outliers, while the median is not.

So in this case, since the distribution is not symmetrical and has an outlier, it is better to use the median to describe the center of the distribution.

E)

The standard deviation of a distribution is a quantity used to describe the spread of the distribution. It is calculated as:

$\sigma = \sqrt{\frac{\sum (x_i-\bar x)^2}{N}}$

where

$\sum (x_i-\bar x)^2$ is the sum of the residuals

N is the number of values in the dataset (in this case, 25)

$\bar x$ is the mean value of the dataset

The presence of an outlier in the distribution affects significantly the standard deviation, because it changes significantly the value of the sum $\sum (x_i-\bar x)^2$ .

In fact, in this problem,

$\sum (x_i-\bar x)^2=84.64$

So the standard deviation is

$\sigma = \sqrt{\frac{84.64}{25}}=1.84$

Instead, if we remove the outlier from the dataset,

$\sum (x_i-\bar x)^2=45.63$

So the standard deviation is

$\sigma = \sqrt{\frac{45.63}{24}}=1.38$

So, the standard deviation is much higher when the outlier is included.

F)

The interquartile range (IQ) of a dataset is the difference between the 3rd quartile and the 1st quartile:

$IQ=Q_3-Q_1$

Where:

$Q_3$ = 3rd quartile is the value of the dataset for which 25% of the values are above $Q_3$ , and 75% of the values are below it

$Q_1$ = 1st quartile is the value of the dataset for which 75% of the values are above $Q_1$ , and 25% of the values are below it

In this dataset, the 1st and 3rd quartiles are the 7th and the 18th values, respectively (since we have a total of 25 values), so they are:

$Q_1=0\\Q_3=2$

So the interquartile range is

$IQ=2-0 = 2$

If the outlier is removed, $Q_1, Q_3$ do not change, therefore the IQ range does not change.

G)

The spread of a distribution can be described by using two different quantities:

- If the distribution is quite symmetrical and has no tails/outliers, then the standard deviation is a good value that can be used to describe the spread of the distribution.

- On the other hand, if the distribution is not very symmetrical and has tails/outliers, the interquartile range is a better estimator of the spread of the distribution, because the standard deviation is very affected by the presence of outliers, while the IQ range is not is not.

So in this case, since the distribution is not symmetrical and has an outlier, it is better to use the IQ range to describe the spread of the distribution.

5 0

3 years ago