Answer:
1)
Weights: =0.06321578
Ages: =0.06980003
2) A) Ages are more variable than weights for all wide receivers on this team
Step-by-step explanation:
The coefficient of variation is calculated as follows
where s is the sample standard deviation and x bar is the sample mean,
where
∑(xi-x bar)^2/(n-1)
xi=i observation, n is the sample size
and, x bar = ∑(xi) / n
The differential equation describing represent the given equation is
Total number of people in company N = 6000 and Total people involved in bribery P
Here Number of people not affected should be N - P
Now
The differential equation should be
Now we input the value of N
So,
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Answer:
dP/dt = k*(600 - P)*P
Step-by-step explanation:
Given:
- Total number of people in company N = 6000
- Total people involved in bribery P
The rate at which people become involved in a corporate bribing scheme is jointly proportional to the number of people already involved and the number of people who are not yet involved.
Find:
Write a differential equation
Solution:
- The following differential equation can be used to describe the situation above:
Number of people not affected = N - P
- Hence we can write a differential equation:
dP/ dt = k *( N - P )*P
- input the value of N:
dP/dt = k*(600 - P)*P
Answer:
a)
b)
The significance level would be
So the p value is higher than the significance level given 0.05, so then we can conclude that we FAIL to reject the null hypothesis that the mean after minus the mean before is lower or equal than 0.
So we don't have enoug evidence to conclude that the course actually increased scores on the driving exam
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation :
x=test value before , y = test value after
x: 83 89 93 77 86 79
y: 87 88 91 77 93 83
Part a
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
The first step is calculate the difference and we obtain this:
d: 4, -1, -2, 0, 7, 4
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
The 4 step is calculate the statistic given by :
Part b
The next step is calculate the degrees of freedom given by:
Now we can calculate the p value, since we have a left tailed test the p value is given by:
The significance level would be
So the p value is higher than the significance level given 0.05, so then we can conclude that we FAIL to reject the null hypothesis that the mean after minus the mean before is lower or equal than 0.
So we don't have enoug evidence to conclude that the course actually increased scores on the driving exam
Answer:
a) P ( X < 91 ) = 0.9927
b) P ( 65 < X < 91 ) = 0.6585
c) P(81 < X < 89 ) =0.0781
d) X = 83.8
Step-by-step explanation:
Given:
- Mean of the distribution u = 69
- standard deviation sigma = 9
Find:
a. what is the probability of getting a grade of 91 or less on this exam?
b. What percentage of students scored between 65 and 89?
c. What percentage of students scored between 81 and 89?
d. Only 5% of the students taking the test scored higher than what grade?
Solution:
- We will declare a random variable X denoting the score that a student gets on a final exam. So,
X ~ N ( 69 , 9 )
- After defining our variable X follows a normal distribution. We can compute the probabilities as follows:
a) P ( X < 91 ) ?
- Compute the Z-score value as follows:
Z = (91 - 69) / 9 = 2.4444
- Now use the Z-score tables and look for z = 2.444:
P( X < 91 ) = P ( Z < 2.4444) = 0.9927
b) P ( 65 < X < 89 ) ?
- Compute the Z-score values as follows:
Z = (89 - 69) / 9 = 2.2.222
Z = (65 - 69) / 9 = -0.4444
- Now use the Z-score tables and look for z = 2.222 and Z = -0.4444:
P(65 < X < 89 ) = P ( -0.444< Z < 2.2222) = 0.6585
b) P ( 81 < X < 89 ) ?
- Compute the Z-score values as follows:
Z = (89 - 69) / 9 = 2.2.222
Z = (81 - 69) / 9 = 1.3333
- Now use the Z-score tables and look for z = 2.222 and Z = 1.333:
P(81 < X < 89 ) = P ( 1.333< Z < 2.2222) = 0.0781
c) P ( X > a ) = 0.05 , a?
- Compute the Z-score values as follows:
Z = (a - 69) / 9 = q
- Now use the Z-score tables and look for z value that corresponds to:
P( X > a ) = P ( Z > q ) = 0.05
- The corresponding Z-value is: q = 1.6444
Hence,
Z = (a - 69) / 9 = 1.644
a = 83.8
Answer:
A
Step-by-step explanation:
The answer is A The mean is the average driving performance index value, B is the definition of mode, C is the definition of the median or percentile 50.
Answer:
A. The mean is the average driving performance index value.
Step-by-step explanation:
Mean is a measure of central tendency, it is the average of a set of data. It can be derived by summing the data and dividing the sum by the number of data.
A. The mean is the average driving performance index value. - mean
B. The mean is the driving performance index value that occurs most often in the data set. - Mode
C. The mean is the driving performance index value such that half of the values in the data set are higher than it. - median
Therefore, the mean is the average driving performance index value(A)
Answer:
t =1.453 decades from 1980 i.e in year 1994.5
Step-by-step explanation:
Given:
- Population @ year 1980 P = 678.97 thousands.
- Population @ year 2000 P = 776.73 thousands.
- The rate of increase is linear - constant rate.
Find:
As the population of San Francisco was revitalizing, for what value of the independent variable t did it reach 750 thousand ?
Solution:
- Develop an expression of population P as a function of time t in decades elapsed from year 1980 on-wards
- The linear expression can take a form of :
P(t) = m*t + C
- Where, m is the rate of increase.
C is the initial population.
- Formulate m:
m = (776.73 - 678.97) / 2 = 48.88
- Formulate C:
C = P (@ 1980) = 678.97
- Evaluate P(t) = 750:
P(t) = 48.8*t + 678.97
750 = 48.8*t + 678.97
t = 71.03/48.8
t =1.453 decades
Answer:
The dependent variable is pounds lost for each group.
Step-by-step explanation:
We are given the following in the question:
A hypothesis is done to measure the average number of pounds lost based on the fact whether a person follows a low carb diet or high carb diet.
Dependent and independent variable:
For the hypothesis:
Independent variable:
Participants of a group follows a low-carb or high carb diet for 4 weeks.
Dependent Variable:
average number of pounds lost for each group
Thus, the dependent variable is pounds lost for each group.
Answer:
The question is not complete because we were not given the data that represent the miles per gallon of a random sample of smart cars with a three cylinder, 1.0-liter engine.
However, we are going to assume some data below such that whatever data is latter provided, the solution to the question follows the sama procedure and pattern.
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
Now to solve for
(a) which is to compute the Z-score corresponding to the individual who obtained 37.837.8 miles per gallon.
Therefore, the value of z-score is calculated as follows,
μ = Σ lin (n) lin (i=1) X₁ / n → 933.1 /24 → 38.88
σ = √ Σ lin (n) lin (i=1) X₁² - nX⁻²/ n - 1 → 3.61
z = X - μ / σ → 37.8 - 38.88/3.61 = − 0.299
Therefore, the value of z-score is -0.299.
(b) Considering the fact that the values are in ascending order is given as,
Recalling the values: 31.5, 36, 37.8 ,38.5, 40.1 ,42.2, 34.2 ,36.2, 38.1, 38.7, 40.6 ,42.5, 34.7, 37.3 ,38.2, 39.5 ,41.4, 43.4, 35.6, 37.6 ,38.4 ,39.6 ,41.7, 49.3
Q₁ = ( n+1/4)th value → (24+1/4)th value → 6.25th value → 36.2 + 0.25 ∗ ( 37.3 − 36.2 ) => 36.47
M = ( n+1/2)th value → (24+1/2)th value = (24+1/4)th value => 12.5 t h v a l u e => 38.4 + 38.5/2 = 38.45
Q₃ = 3( n+1/4)th value → 3(24+1/4)th value => 18.75 t h v a l u e => 40.6 + 0.75 ∗ ( 41.4 − 40.6 ) => 41.2
(c) I n t e r q u a r t i l e r a n g e = Q ₃ − Q ₁ => 41.2 − 36.47 => 4.25
Therefore, the IQR value is measure of spread of data, and here the value of IQR = 4.25.
(d) L o w e r f o u r t h = Q₁− 1.5 ( I Q R ) => 36.75 − 1.5 ( 4.25 ) => 30.375 U p p e r f o u r t h = Q ₃ + 1.5 ( I Q R ) => 41 + 1.5 ( 4.25 ) => 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
The table for the entire problem is given as,
Z- Score -0.299
Q₁ 36.47
Q₂ 38.45
Q₃ 41.2
IQR 4.25
Lower fourth 30.375
Upper fourth 47.375
Answer:
Step-by-step explanation:
There is no y intercept so start from the (0,0) and count 3 up and 2 to the left and just make a straight line with those points
Answer:
Step-by-step explanation:
Collecting all the x terms together on the left side,
Simplifying the terms,
Moving all the x terms to one side of the equation,
The required solution of the equation is
Answer:
6x-3=-3x+4
9x-3=4
9x=4
x=2.25
Step-by-step explanation:
Answer:
0.50
Step-by-step explanation:
The question asks you to apply the classical method of computing probability. In this method, prior events do not interfere in the likelihood of an event happening in the future, instead it states that every possible outcome is equally likely to happen.
In this case there are only two possible outcomes: purchase or not purchase a computer. Therefore, the likelihood that the next customer will purchase a computer is 50% or 0.50.