Find the volume of the sphere. r = 3 cm. V= cm^3

The table showing the stock price changes for a sample of 12 companies on a day is contained in the Excel file below.

AfilCa [17]

Answer:

(a) The sample variance for the daily price change is 0.2501.

(b) The sample standard deviation for the daily price change is 0.5001.

(c) The 95% confidence interval estimates of the population variance is (0.1255, 0.7210).

Step-by-step explanation:

Let the random variable X denote the stock price changes for a sample of 12 companies on a day.

The data provided is:

X = {0.82 , 1.44 , -0.07 , 0.41 , 0.21 , 1.33 , 0.97 , 0.30 , 0.14 , 0.12 , 0.42 , 0.15}

(a)

The formula to compute the sample variance for the daily price change is:

$s^{2}=\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}$

The sample mean is computed using the formula:

$\bar X=\frac{1}{n}\sum\limits^{12}_{i=1}{X_{i}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample mean and sample variance are:

$\bar X$ =AVERAGE(A2:A13)

$s^{2}$ =VAR.S(A2:A13)

Thus, the sample variance for the daily price change is 0.2501.

(b)

The formula to compute the sample standard deviation for the daily price change is:

$s=\sqrt{\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample standard deviation is:

$s$ =STDEV.S(A2:A13)

Thus, the sample standard deviation for the daily price change is 0.5001.

(c)

The (1 - α)% confidence interval for population variance is:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

Compute the critical value of Chi-square for α = 0.05 and (n - 1) = (12 - 1) = 11 degrees of freedom as follows:

$\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2,11}=21.920$

$\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{(1-0.05/2),11}=\chi^{2}_{0.975,11}=3.816$

*Use a Chi-square table.

Compute the 95% confidence interval estimates of the population variance as follows:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

$=[\frac{(12-1)\times 0.2501}{21.920 } \leq \sigma^{2}\leq \frac{(12-1)\times 0.2501}{3.816} ]$

$=[0.125506\leq \sigma^{2}\leq 0.720938]\\\approx [0.1255, 0.7210]$

Thus, the 95% confidence interval estimates of the population variance is (0.1255, 0.7210).

7 0

4 years ago

Aaron and Maria collected shells one morning at the beach. Maria had 3 times as many as Aaron, but they would have the same numb

avanturin [10]

3A = M
A + 8 = M - 6
3A = M

A + 8 = 3A - 6
A + 14 = 3A
14 = 2A
A = 7

M = 3A
M = 3 x 7
M = 21

So overall Aaron had 7 shells, and Maria had 21.

6 0

3 years ago

What is the value of F(x) = 4x+9 When x= 5

Elodia [21]

Answer:

f(5) = 29

Step-by-step explanation:

Step 1: Identify the function

f(x) = 4x + 9

Step 2: Let x equal 5 in the function

f(5) = 4(5) + 9

Step 3: Multiply

f(5) = 20 + 9

Step 4: Add

f(5) = 29

Answer: 29

8 0

4 years ago

Read 2 more answers

Researchers recorded that a certain bacteria population declined from 120,000 to 200 in 36 hours. At this rate of decay, how man

quester [9]

Answer: There will 486 bacteria in 31 hours.

Step-by-step explanation:

The population decay in bacteria is exponential.

Exponential function : $y=Ab^x$ , where A = initial population, b multiplication decay factor, t= time:

As per given:

Initial population: $A=120,000$

After 36 hours, population = $120000(b^{36})=200$

Divide both sides by 120,000 we get

$b^{36}= 0.00167$

Taking natural log on both sides , we get

$36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372$

At x= 31,

$y=120000(0.8372)^{31}=120000\times0.00405234\approx486$

Hence, there will 486 bacteria in 31 hours.

4 0

4 years ago

I really need some help!

igor_vitrenko [27]

-4x = y + 3
y = -4x - 3

The second equation is solved for y.
We'll leave it like that.
Now we solve the first equation for y.

-4x = y + 3

-4x - 3 = y

y = -4x - 3

Write the new form of the first equation followed by the original second equation.

y = -4x - 3
y = -4x - 3

Before we get to the addition method, we see that both equations are the same.

The solution is every real number.

5 0

3 years ago