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The cheerleaders at Lake High School launch T-shirts into the crowd every time the Lakers score a touchdown. The height of the T

Mamont248 [21]

the anser is c because i dont know

6 0

2 years ago

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today

Ierofanga [76]

Answer:

a) We can find the z score for the value of 225 and we got:

$z = \frac{225-204}{55}=0.382$

And we can find this probability with the complement rule:

$P(z>0.382)=1-P(z$

b) $z = \frac{140-204}{55}=-1.164$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

c) $P(200$

And we can find this probability with this difference:

$P(-0.072$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.072$

d) For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.2$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.8 of the area on the left and 0.2 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.2

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$a=204 +0.842*55=250.31$

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the costs of a population, and for this case we know the distribution for X is given by:

$X \sim N(204,55)$

Where $\mu=204$ and $\sigma=55$

We are interested on this probability

$P(X>225)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

We can find the z score for the value of 225 and we got:

$z = \frac{225-204}{55}=0.382$

And we can find this probability with the complement rule:

$P(z>0.382)=1-P(z$

Part b

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$z = \frac{140-204}{55}=-1.164$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

Part c

$P(200$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(200$

And we can find this probability with this difference:

$P(-0.072$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.072$

Part d

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.2$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.8 of the area on the left and 0.2 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.2

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$a=204 +0.842*55=250.31$

5 0

3 years ago

pen costs twice as much as a pencil. The total cost of 1 1 pen and 1 1 pencil is $2.10 $ 2 . 10 . If p represents the cost of 1

dybincka [34]

Answer : The equation could you use to find p is, $2p+p=2.10$

Step-by-step explanation :

Let the cost of 1 pen be, 'x'

and the cost of 1 pencil is, 'p'

As we are given that total cost of 1 pen and 1 pencil is $2.10. The equation will be:

$x+p=2.10$ ............(1)

And we have also given that the pen costs twice as much as a pencil. The equation will be:

$x=2p$ ............(2)

Now put the equation 2 in equation 1, we get:

$x+p=2.10$

$2p+p=2.10$

Thus, the equation could you use to find p is, $2p+p=2.10$

3 0

3 years ago

Read 2 more answers

How to simplify 5 cubed

alex41 [277]

Answer:

125

Step-by-step explanation:

Steps to Solving the Problem

So let's say you have five friends who who are each going to pay you five dollars for the next five days. You can figure out how much money you will receive by calculating five cubed or five to the third power. This will tell us how much money you will get because you will multiply 5 by 5 by 5 or 5 cubed.

To start, you need to turn words into numbers by figuring out the base and exponent. An exponent is the number after the ^ which tells you how many times to multiply the base number by itself. The base number comes before the ^. When five is cubed, five is the base number which will show up before the ^.

Three is the exponent and will be the number after the ^. We know three is the exponent because of the word 'cubed,' which always represents the number three.

We can write out five cubed as:

5^3

Once the exponent and base are figured out, we need to write out the long version, which shows all the multiplication being done. In this case, the exponent of three tells us to multiply five by itself three times.

5 x 5 x 5

This shows us 5 friends multiplied by $5 multiplied by 5 days.

From here, multiply the numbers out to get the final answer. Multiply two numbers at a time to so you don't make a mistake.

5 x 5 = 25

25 x 5 = 125

6 0

3 years ago

A magazine provided results from a poll of 500500 adults who were asked to identify their favorite pie. Among the 500500 respon

Komok [63]

Answer:

99% confidence interval is wider as compared to the 80% confidence interval.

Step-by-step explanation:

We are given that a magazine provided results from a poll of 500 adults who were asked to identify their favorite pie.

Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as plus or minus ±3 percentage points.

The pivotal quantity for the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who chose chocolate pie = 14%

n = sample of adults = 500

p = true proportion

Now, the 99% confidence interval for p = $\hat p \pm Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

Here, $\alpha$ = 1% so $(\frac{\alpha}{2})$ = 0.5%. So, the critical value of z at 0.5% significance level is 2.5758.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.03 for 99% interval.

So, 99% confidence interval for p = $0.14 \pm2.5758 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

= [0.14 - 0.03 , 0.14 + 0.03]

= [0.11 , 0.17]

Similarly, 80% confidence interval for p = $0.14 \pm 1.2816 \times \sqrt{\frac{0.14(1-0.14)}{500} }$

Here, $\alpha$ = 20% so $(\frac{\alpha}{2})$ = 10%. So, the critical value of z at 10% significance level is 1.2816.

Also, Margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$ = 0.02 for 80% interval.

So, 80% confidence interval for p = [0.14 - 0.02 , 0.14 + 0.02]

= [0.12 , 0.16]

Now, as we can clearly see that 99% confidence interval is wider as compared to 80% confidence interval. This is because more the confidence level wider is the confidence interval and we are more confident about true population parameter.

5 0

3 years ago