Leyla drops a penny from a height of 150m.

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

lions [1.4K]

Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

Step-by-step explanation:

Previous concepts

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

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

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:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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

And replacing into equation (b) the values from part a we got:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

6 0

2 years ago

The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total sales were $1050. How

S_A_V [24]

We know the total tickets sold = 400. Let x be the number of adult tickets sold. That means 400 - x is the number of student tickets. The revenue from adult tickets will be $3 * x, which we can call 3x. The revenue from student ticks will be $2 * (400 - x), or 800 - 2x. The total revenue is $1050, so that means: 3x + (800 - 2x) = 1050. Removing the parentheses: 3x + 800 - 2x = 1050 Subtracting 800 from both sides: 3x - 2x = 250 Simplifying the left side: x = 250, which is the number of adult tickets. 400-x = student tickets = 400-250 = 150. ALWAYS check! In this case, check the revenue: 3x = 3(250) = 750 2(150) = 300 750 + 300 = 1050. Check!

5 0

2 years ago

cinema A sells a twelve pack of moive passes for $66. Cinema B selles a five pack of moive passes for $28. Find the cost per moi

nekit [7.7K]

CINEMA A sells each movie pass for $5.50, and CINEMA B sells each movie pass for $5.60.

To find the cost of each pass in Cinema A, all you would have to do it divide 66 by 12, where you would get 5.5, which in other words would be $5.50. And to find the cost of each pass in Cinema B, you wound divide 28 by 5,and you would get 5.6, which is in other words, $5.60.

5 0

3 years ago

I need help with this

Ostrovityanka [42]

Answer:

Christy is correct

Step-by-step explanation:

you dont say the numbers in words all the time, so it makes a lot more sense.

5 0

3 years ago

Use the formula A = h(b1 + b2).<br> What is the area of the trapezoid?<br> square units

deff fn [24]

Only use h=trapezoid's height.

b=base

4 0

3 years ago

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