Someone help me please

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

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

Solution to the problem

For this case we can find the sample proportion for each observation with the following formula:

$\hat p = \frac{X}{n}$

Where X represent the number of returns and n =100 for each case since the standard value used. Using the last formula we got:

$p_1 = \frac{10}{100}=0.1$

$p_2 = \frac{9}{100}=0.09$

$p_3 = \frac{11}{100}=0.11$

$p_4 = \frac{7}{100}=0.07$

$p_5 = \frac{3}{100}=0.03$

$p_6 = \frac{12}{100}=0.12$

$p_7 = \frac{8}{100}=0.08$

$p_8 = \frac{4}{100}=0.04$

$p_9 = \frac{6}{100}=0.06$

$p_{10} = \frac{11}{100}=0.11$

And now witht those values we can find the sample mean of proportions with the following formula:

$hat p = \frac{\sum_{i=1}^n p_i}{n}= \frac{0.1+0.09+0.11+0.07+0.03+0.12+0.08+0.04+0.06+0.11}{10}=0.081$

And we can find the standard error with the following formula:

$SE= \sqrt{\frac{\hat p (1-\hat p)}{n}}=\sqrt{\frac{0.081(1-0.081)}{10}}=0.0863$

So then the best option on this case is given by:

E) .0863

6 0

3 years ago

Joannie lent $200 to her sister. Four years later, her sister repaid her in full with $228. What simple annual interest rate did

vodomira [7]

Ok, so lets convert all the percents into decimals to help us solve this problem

A 3.0%= 0.03

B 3.5%= 0.035

C 4.0%= 0.04

D 4.5%= 0.045

Now, we can multiply $200 by all the decimals we just converted to see which one will add up to $208

200*0.03= 6-------200+6=206 (this is not equal to 208 so it's not A)

200*0.035=7--------200+7= 207 (Still does not equal 208, so it's not B)

200*0.04= 8---------200+8=208 C is your answer

7 0

3 years ago

two planes, which are 1965 miles apart, fly toward each other. their speeds differ by 55mph. if they pass each other other in 3

Alexus [3.1K]

The speed of the planes are 300 miles per hour and 355 miles per hour.

Solution:

Given, Two planes are 1965 miles apart, flying toward each other.

Their speeds differ by 55 mph.

They pass each other in 3 hours,

We have to find what is the speed of each?

Let the speed of 1st plane be s miles per hour, then speed of the other plane will be s + 55 miles per hour.

And, distance travelled by 1st plane be d, then distance travelled by other plane will be 1965 – d miles

Now, we know that, distance = speed $\times$ time

So, for 1st plane ⇒ $\mathrm{d}=\mathrm{s} \times 3$

For 2nd plane ⇒ $1965-d=(s+55) \times 3$

By using 1st plane equation

1965 – 3s = 3s + 165

1965 – 165 = 3s + 3s

6s = 1800

s = 300

So, speed of 1st plane is 300 miles per hour, then speed of 2nd plane will be 300 + 55 = 355 miles per hour.

Hence, the speed of the planes are 300 miles per hour and 355 miles per hour.

4 0

4 years ago