Solve the two step inequality 3p+2≥−10

Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver’s license. Twenty-five years later (in 2008) that perc

Dima020 [189]

Answer:

a) $ME=1.96\sqrt{\frac{0.87 (1-0.87)}{1200}}=0.019$

b) $ME=1.96\sqrt{\frac{0.75 (1-0.75)}{1200}}=0.0245$

c) On this case it's not the same since the proportion estimated for 1983 it's different from the proportion estimated for 2008. So since the margin of error depends of $\hat p$ the margin of error change for part a and b.

Step-by-step explanation:

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".

The population proportion have the following distribution

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

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

If we replace the values into equation (a) for 1983 we got:

$ME=1.96\sqrt{\frac{0.87 (1-0.87)}{1200}}=0.019$

Part b

Since is the same confidence level the z value it's the same.

If we replace the values into equation (a) for 2008 we got:

$ME=1.96\sqrt{\frac{0.75 (1-0.75)}{1200}}=0.0245$

Is the margin of error the same in parts (a) and (b)? Why or why not?

On this case it's not the same since the proportion estimated for 1983 it's different from the proportion estimated for 2008. So since the margin of error depends of $\hat p$ the margin of error change for part a and b.

3 0

3 years ago

9/16x = 3/4 how do you do it if you’re solving for x

ruslelena [56]

Answer:

$x=\frac{3}{4}$

Step-by-step explanation:

Whenever we have 2 fractions equal to each other, we first cross multiply, then take variables to one side and numbers to other side and use basic algebra to solve for the variable [here, it is x].

The process is shown below:

$\frac{9}{16x}=\frac{3}{4}\\9*4=16x*3\\36=48x\\x=\frac{36}{48}=\frac{3}{4}$

So, x = 3/4

7 0

3 years ago

As a town gets smaller, the population of its high school decreases by 4% each year. The senior class has 320 students now. In

Mice21 [21]

Answer:

c(n) = 320·0.96^n
28 years

Step-by-step explanation:

Each year, the class size is multiplied by 1 - 4% = 96% = 0.96. After n years, it has been multiplied by that number n times. Repeated multiplication is signified using an exponent.

Class size (c) can be modeled by ...

c(n) = 320·0.96^n

__

You want to find n such that c(n) = 100. Put in that value and solve.

100 = 320·0.96^n

100/320 = 0.96^n . . . . . . . divide by 320

log(100/320) = n·log(0.96) . . . . . . . take logs

log(100/320)/log(0.96) = n ≈ 28.4932

In about 28 years, the class will have 100 students.

8 0

3 years ago

Reduce the following fractto their lowest form

Keith_Richards [23]

Answer:

a) 3/16

b) 8/7

Step-by-step explanation:

i think the idea there was just simplifying the fractions.

6 0

2 years ago

Factorise the following: x^2-14x+48

Novosadov [1.4K]

Answer:

(x-8)(x-6)

Step-by-step explanation:

To factor this, you need the numbers that will multiply together to give you the third number (48 in this case) and add together to give you the second number (-14). -8 * -6 = 48. -8 + -6 = -14

6 0

2 years ago

Read 2 more answers