Explain how you could use Distributive Property and mental math to find 5 x 198

A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale,

Lyrx [107]

Answer:

a) The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =85.82-81.90=3.92$

b) $SE=\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=0.975$

And the Margin of error is given by:

$Me= z_{\alpha/2} * SE=1.96*0.975=1.910$

c) The 95% confidence interval would be given by $2.009 \leq \mu_1 -\mu_2 \leq 5.83$ .

Step-by-step explanation:

Notation and previous concepts

$n_1 =35$ represent the sample of ships that carry fewer than 500 passengers

$n_2 =44$ represent the sample of ships that carry 500 or more passengers

$\bar x_1 =85.82$ represent the mean sample of of ships that carry fewer than 500 passengers

$\bar x_2 =81.90$ represent the mean sample of of ships that carry 500 or more passengers

$\sigma_1 =4.55$ represent the population deviation of ships that carry fewer than 500 passengers

$\sigma_2 =3.97$ represent the sample deviation of ships that carry 500 or more passengers

$\alpha=0.05$ represent the significance level

Confidence =95% or 0.95

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{(\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2})}$ (1)

Part a

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =85.82-81.90=3.92$

Part b: At 95% confidence, what is the margin of error?

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

The standard error is given by the following formula:

$SE=\sqrt{(\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2})}$

And replacing we have:

$SE=\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=0.975$

And the Margin of error is given by:

$Me= z_{\alpha/2} * SE=1.96*0.975=1.910$

Part c: What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

Confidence interval

Now we have everything in order to replace into formula (1):

$3.92-1.96\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=2.009$

$3.92+1.96\sqrt{(\frac{4.55^2}{35}+\frac{3.97^2}{44})}=5.830$

So on this case the 95% confidence interval would be given by $2.009 \leq \mu_1 -\mu_2 \leq 5.83$ .

7 0

3 years ago

Antonio is having a pizza party for his birthday. He ordered 5 large pizzas, which have a total of 40 slices. He invited 8 peopl

love history [14]

Answer: the number of slices that each person will get is 4 4/9

Step-by-step explanation:

Antonio ordered 5 large pizzas, which have a total of 40 slices.

He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, it means that the pizza would be divided among 9 people(Antonio and 8 friends = 9 people).

The number of slices that each of them will get would be

40/9 = 4 4/9 slices

4 0

3 years ago

Math question 10 points

Dimas [21]

Answer: (a)

Step-by-step explanation:

the last step is

clear x

X=15.9/6.36

the answer is 5/2 or 2.50

5 0

2 years ago

120 caleriess in 2 servings 360 caleries in 6 servings

lutik1710 [3]

Answer:

60 calories per serving

Step-by-step explanation:

Divide to find the unit rate of calories per serving.

120 / 2 = 60

360 / 60 = 60

Best of Luck!

6 0

3 years ago

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Any ideas? I cant understand what its asking and although i'm trying my best i don't get it

Korvikt [17]

Answer:

{ x: x€R | x≤7, x }

Step-by-step explanation:

I think they are asking set builder form for the expression

For any other explaination or enquiry pleas ask me down in comments...

5 0

3 years ago

Read 2 more answers