1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rjkz [21]
2 years ago
6

Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. (Negative value

s should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)
x −36 −26 −15 −4
P(X = x) 0.32 0.36 0.21 0.11
Mean
Variance
Standard deviation
Mathematics
1 answer:
asambeis [7]2 years ago
3 0
<h2>Answer:</h2>

Mean = 24.47

Variance = 108.31

Standard deviation = 10.41

<h2>Step-by-step explanation:</h2>

The probability distribution table has been attached to this response.

<em>(1) To calculate the mean (m)</em>

(a) First multiply each of the values of x by their corresponding probability values.

This is shown in the third column of the table.

(b) The sum of the results in the third column gives the mean of the distribution. i.e

m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44

m = 24.47

<em>(2) To calculate the variance </em> <em>(σ²).</em>

(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e

(x - m)²

The result is shown in the fourth column of the table.

(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e

(x - m)²(P(X = x))

The result is shown in the fifth column of the table.

(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e

σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923

σ² = 108.3091

σ² = 108.31      [to 2 decimal places]

<em>(3) To calculate the standard deviation (σ)</em>

The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.

σ = √σ²

σ = \sqrt{108.31}

σ = 10.4072

σ = 10.41        [to 2 decimal places]

You might be interested in
Can anyone help me with this please???
yanalaym [24]
Triangle = 3, Square = -1, Star = 5
8 0
2 years ago
Find the surface area of a rectangular figure
Ann [662]

Answer:

360ft^2

hope it's helpful ❤❤❤❤

THANK YOU.

4 0
2 years ago
Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol
Dima020 [189]

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

And rounded up we have that n=2663

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.025 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

We can assume an estimated proportion of \hat p =0.5 since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

And rounded up we have that n=2663

6 0
3 years ago
10) The figure below is a regular octagon. What is the least number of degrees that the octagon must be rotated clockwise around
kiruha [24]

From the following figure:

Because the center angle measure 45 degrees, we must rotate 3 times 45 degrees to get point D.

In other words, we must rotate

3\cdot45=135

that is 135 degrees clockwise.

6 0
1 year ago
Can someone help me with 34-37??
zzz [600]

Answer:

-3

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • Which equation shows how to use equivalent fractions to evaluate 2 5 + 3 4 5 2 ​ + 4 3 ​ start fraction, 2, divided by, 5, end f
    6·1 answer
  • WHAT IS 7.5% OF 80? ROUND TO THE NEAREST HUNDRETH
    14·2 answers
  • Natalie just rented an apartment for 900$ a month she was told that the rent will increase 5.5% each year about how much will he
    14·1 answer
  • Which angles are shown in the diagram?
    14·2 answers
  • What is the greatest common factor of 14 and 35
    13·2 answers
  • Determine the commutators of the operators a and a+,where a = (x + ip)/2 ^1/2 and a+ = (x - ip)/ 2 ^1/2
    6·1 answer
  • 4, Write an inequality to compare the numbers 7 1/8 v50
    9·1 answer
  • What is the value of X?
    11·2 answers
  • Old McDonald had a farm. In one pen the old farmer had chickens and bulls together. In that pen there were 40 animals in total,
    15·1 answer
  • A group of 5 friends went to a baseball
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!