Please answer correctly !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!

A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is n

Olegator [25]

Answer:

i) $2 - 1.64 \frac{0.1}{\sqrt{16}}= 1.959$

$2 + 1.64 \frac{0.1}{\sqrt{16}}= 2.041$

So then the 90% confidence interval is given by (1.959, 2.041)

ii) Figure attached

iii) $ME= 1.64 *\frac{0.1}{\sqrt{16}}= 0.041$

Step-by-step explanation:

Previous concepts

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 confidence interval is given by this formula:

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

And for a 90% of confidence the significance is given by $\alpha=1-0.9=0.1$ , and $\frac{\alpha}{2}=0.05$ . Since we know the population standard deviation we can calculate the critical value $z_{0.05}= \pm 1.64$

We know the folllowing data:

$\bar X = 2$ represent the sample mean

$\sigma = 0.1$ represent the population deviation

n =16 represent the sample size

Part i)

If we replace the values given into formula (1) we got:

$2 - 1.64 \frac{0.1}{\sqrt{16}}= 1.959$

$2 + 1.64 \frac{0.1}{\sqrt{16}}= 2.041$

So then the 90% confidence interval is given by (1.959, 2.041)

Part ii)

Figure attached. We have the illustration for the confidence interval obtained.

Part iii)

The margin of error is given by:

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

And if we replace we got:

$ME= 1.64 *\frac{0.1}{\sqrt{16}}= 0.041$

3 0

3 years ago

Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Gnesinka [82]

Cos^4(x) =
(cos²x)² =
(1-sen²x)² =
1² - 2*1*sen²x + sen^4x =
1 - 2sen²x + sen^4x

6 0

3 years ago

Can someone find the slope of these 2 equations

Blababa [14]

The slope is 4 and 3

5 0

3 years ago

Find the 20th, 40th, 60th, and 80th percentiles of the standard normal distribution. Round the answers to two decimal places.

Fed [463]

To answer the question above, we have to use the z-score percentile table for the standard normal distribution. It shows:
The 20th percentile = - 0.84
The 40th percentile = - 0.25
The 60th percentile = 0.25
The 80th percentile = 0.84

I hope my answer helped you. Have a nice day!

3 0

3 years ago

9. Determine whether or not the number 257 is prime.

Sladkaya [172]

Answer:

257 is prime.

Step-by-step explanation:

To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.

In this case, √257 = 16.03 so we just need to see if 257 is divisible by <u>2, 3, 5, 7, 11 and 13</u> (the prime numbers that come before 16)

257 is odd, so it is not divisible by 2.

The sum of its digits is 14, therefore, it is not divisible by 3.

257 ends in 7, therefore it's not divisible by 5.

257/ 7 = 36.71 so it's not divisible by 7.

257/ 11 = 23.36 so it's not divisible by 11

Finally 257 / 13= 19.76 so it's not divisible by 13.

Therefore, 257 is prime.

7 0

3 years ago