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Suppose monthly rental prices for a one-bedroom apartment in a large city has a distribution that is skewed to the right with a population mean of $880 and a standard deviation of $50. (a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?
(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Answers

Answer 1

Answer:

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

$\mu = 880, \sigma = 50, n = 30, s = (50)/(√(30)) = 9.1287$

This probability is 1 subtracted by the pvalue of Z when X = 900.

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (900 - 880)/(9.1287)$

$Z = 2.19$

$Z = 2.19$ has a pvalue of 0.9857

1 - 0.9857 = 0.0143

1.43% probability that the sample mean rent price will be greater than $900

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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.2 years and a standard deviation of 0.6 years. He then randomly selects records on 38 laptops sold in the past and finds that the mean replacement time is 3.9 years. Assuming that the laptop replacement times have a mean of 4.2 years and a standard deviation of 0.6 years, find the probability that 38 randomly selected laptops will have a mean replacement time of 3.9 years or less.

Answers

Answer: 0.0010

Step-by-step explanation:

Given the following :

Population Mean(m) = 4.2 years

Sample mean (s) = 3.9

Standard deviation (sd) = 0.6

Number of samples (n) = 38

Calculate the test statistic (z) :

(sample mean - population mean) / (sd / √n)

Z = (3.9 - 4.2) / (0.6 / √38)

Z = (- 0.3) / (0.6 / 6.1644140)

Z = -0.3 / 0.0973328

Z = - 3.0822086

Z = - 3.08

From the z table :

P(Z ≤ - 3.08) = 0.0010

Final answer:

The probability that the mean replacement time of a random sample of 38 laptops is 3.9 years or less, assuming the true mean replacement time is 4.2 years, is approximately 0.0038 or 0.38%

Explanation:

To solve this problem, we will use the formula for the Z score of a sample mean:
Z = (x - µ) / (σ/ √n)

In this case, the mean µ is 4.2 years, the standard deviation σ is 0.6 years, the sample mean x is 3.9 years, and the sample size n is 38.

Substituting the given values into the formula, we get:
Z = (3.9 - 4.2) / (0.6/√38) = -2.67.

We can then look up this Z score in the Z score table or use statistical software to find the corresponding probability. The probability associated with Z = -2.67 is approximately 0.0038. This means there's about a 0.38% chance that the mean replacement time of a random sample of 38 laptops will be 3.9 years or less, assuming the true mean replacement time is 4.2 years.

Learn more about Probability here:

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Jamal is comparing his transportation options for an upcoming trip. He’s considering a rental car and a taxi service. Based on his planned routes during his trip, he expects a taxi service would cost about $128. Jamal could also get a rental car for a daily rate and unlimited miles. If Jamal’s trip will last 4 days and he expects to pay about $24 for gas, which graph shows the range of car rental rates that would be cheaper than the taxi service?

Answers

Answer:

Graph A

Step-by-step explanation:

Say that the car rental rate stands for c dollars ( $ ). We know that Jamal's trip lasts for 4 days, paying $ 24 in expenses for gas, and $ 128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality.

______

The big key here is the part " which graph shows the range of car rental rates that would be cheaper than the taxi service. " Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( $ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,

24 + 4c < 128 - Subtract 24 from either side,

4c < 104 - Divide by 4 on either side, isolating c,

c < 26

The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.

______

The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.

Answer:

A is the answer

Step-by-step explanation:

Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $500

Answers

Answer:

$z = (500-520)/((90)/(√(100)))= -2.22$

And we can find this probability using the normal standard distribution and we got:

$P(z<-2.22) =0.0132$

Step-by-step explanation:

For this case we have the foolowing parameters given:

$\mu = 520$ represent the mean

$\sigma =90$ represent the standard deviation

$n = 100$ the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

$\bar X \sim N(\mu , (\sigma)/(√(n)))$

And we want to find this probability:

$P(\bar X <500)$

We can use the z score formula given by:

$z = (500-520)/((90)/(√(100)))= -2.22$

And we can find this probability using the normal standard distribution and we got:

$P(z<-2.22) =0.0132$

Graph please!!!!
y = 4x - 10

Answers

Answer:

(2,5; 0)

(0: - 10)

Please help so urgent

Answers

Answer:

Option E. None of the above.

Step-by-step explanation:

From the question given above, the following data were obtained:

f(x) = (x – 5)/(2x + 3)

Inverse of f(x) => f¯¹(x) =?

Recall:

When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e

f(x) × f¯¹(x) = 1

With the above information, we can determine the inverse of function given above as follow:

f(x) = (x – 5)/(2x + 3)

Inverse of f(x) => f¯¹(x) =?

f(x) × f¯¹(x) = 1

(x – 5)/(2x + 3) × f¯¹(x) = 1

f¯¹(x)(x – 5) / (2x + 3) = 1

Cross multiply

f¯¹(x)(x – 5) = (2x + 3)

Divide both side by (x – 5)

f¯¹(x) = (2x + 3) / (x – 5)

Thus, the inverse of the function is (2x + 3) / (x – 5).

Option E gives the correct answer to the question.

Pleeease open the image and hellllp me

Answers

1. Rewrite the expression in terms of logarithms:

$y=x^x=e^(\ln x^x)=e^(x\ln x)$

Then differentiate with the chain rule (I'll use prime notation to save space; that is, the derivative of y is denoted y' )

$y'=e^(x\ln x)(x\ln x)'=x^x(x\ln x)'$

$y'=x^x(x'\ln x+x(\ln x)')$

$y'=x^x\left(\ln x+\frac xx\right)$

$y'=x^x(\ln x+1)$

2. Chain rule:

$y=\ln(\csc(3x))$

$y'=\frac1{\csc(3x)}(\csc(3x))'$

$y'=\sin(3x)\left(-\cot^2(3x)(3x)'\right)$

$y'=-3\sin(3x)\cot^2(3x)$

Since $\cot x=(\cos x)/(\sin x)$ , we can cancel one factor of sine:

$y'=-3(\cos^2(3x))/(\sin(3x))=-3\cos(3x)\cot(3x)$

3. Chain rule:

$y=e^{e^(\sin x)}$

$y'=e^{e^(\sin x)}\left(e^(\sin x)\right)'$

$y'=e^{e^(\sin x)}e^(\sin x)(\sin x)'$

$y'=e^{e^(\sin x)+\sin x}\cos x$

4. If you're like me and don't remember the rule for differentiating logarithms of bases not equal to e, you can use the change-of-base formula first:

$\log_2x=(\ln x)/(\ln2)$