Mackenzie invested $770 in an account paying an interest rate of 6.1% compounded

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

a

$\= x = 18.5$ , $\sigma = 5.15$

b

$15.505 < \mu < 21.495$

c

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

What is z- 4/4 +8 simplified?

vova2212 [387]

Answer:

aw baby naw that not cool

Step-by-step explanation:

3 0

2 years ago

You are making a welding fixture and must cut down a length of copper tubbing from 15 1/8 inches to 8 3/4 inches. If the leftove

Bumek [7]

Answer: $6\dfrac{3}{8}\text{ inches}$

Step-by-step explanation:

Given: Original length = $15\dfrac{1}{8}$ inches

$=\dfrac{8\times15+1}{8}=\dfrac{121}{8}$ inches ( In improper fraction )

Length of piece cut from original = $8\dfrac{3}{4}$ inches

$=\dfrac{4\times8+3}{4}$ $= \dfrac{35}{4}$ inches ( In improper fraction )

Length of piece leftover piece = (Original length ) - (Length of piece cut )

$=\dfrac{121}{8}-\dfrac{35}{4}\\\\=\dfrac{121-2\times35}{8}\\\\=\dfrac{121-70}{8}\\\\=\dfrac{51}{8}\\\\=6\dfrac{3}{8}\text{ inches}$

Hence, the leftover piece will be $6\dfrac{3}{8}\text{ inches}$ long.

6 0

3 years ago

What is the domain of the function graphed below?

vlabodo [156]

Answer:

x < 7

Step-by-step explanation:

the domain of a function defines the valid x values for the function.

as we go from left to right through all possible values of x, we see all values incl. x=-1 are creating a valid function result (y) for this function. until we reach x=7.

the empty ball indicates that there is no y value defined here. and for any value x>7 there is no y value defined.

so, x < 7 is the right one.

5 0

3 years ago

(URGENT) I just need to know how you do this... please give a detailed answer on what to do!

enyata [817]

You simplify the equation and you use a x y chart and once you get all the points from simplifying the equation you graph those points on the graph chart then connect them

4 0

3 years ago