How many square numbers are between 1,000 and 2,000

Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years.

Radda [10]

Answer:

a) Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

b) $\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

c) $\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

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".

$\bar X= 200$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=3$ represent the population standard deviation

n=9 represent the sample size

Part a

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

Part b

The distribution for the sample mean is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

Part c

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

8 0

3 years ago

Suppose that you earned a bachelor's degree and now you're teaching high school. The school district offers teachers the oppor

stepan [7]

Answer:

Step-by-step explanation:

Answer:

a. The amount that is saved at the expiration of the 5 year period is $22,769.20¢

b. The amount of interest is $2,769.20¢

Step-by-step explanation:

Since the amount that is deposited every year for a period of five years is $4,000 and the rate of the interest is 6.5%. We can always calculate the amount that is saved at the expiration of the five years.

We will first state the formula for calculating the future value of annuity:-

Future value of annuity =

$P[\frac{(1 + r)^{t}-1 }{r}]$

Where P is the amount deposited per year.

r is the rate of interest

t is the time or period

and in this case, the actual value of P = $4,000

rate of interest, r is 6.5% = 0.065

time, t is 5 years.

Substituting e, we have:

Fv of annuity =

$4,000[\frac{(1 + 0.065)^{5}-1 }{0.065 }]$

= 4,000 × [((1.065)^5)- 1/0.065]

= 4,000 × [(1.37 - 1)/0.065]

= 4,000 × (0.37/0.065)

= 4,000 × 5.6923

= $22,769.20¢

a. Therefore the amount that is saved at the end of the five (5) years is $22,769.20¢

b. To find the interest, we will calculate the amount of deposit made during the period of five years and subtract the sum from the current amount that is saved ($22,769.29¢).

Since I deposited 4,000 every year for five years, the total amount of deposit I made at the period =

4,000 × 5 = $20,000

The amount of interest is then = $22,769.20¢ - $20,000 = $2,769.20¢

3 0

3 years ago

Solve x2 + 2x + 9 = 0. (2 points) x equals negative 2 plus or minus 4 I square root of 2 x equals negative 2 plus or minus 2 I s

vazorg [7]

Answer:

try the answer C

Step-by-step explanation:

4 0

3 years ago