Mathematics, 12.03.2021 21:50, ctyrector

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month

Answers: 1

Show answers

Answers

0.9974 = 99.74% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month.

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 normal distributions can be 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:

$Z = \frac{X - \mu}{\sigma}$

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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 per month.

This means that $\mu = 2350, \sigma = 260$

Sample of 65 one-bedroom apartments

65>30, which means that the sampling distribution of the sample means will be approximately normal. Also, $n = 65, s = \frac{260}{\sqrt{65}} = 32.249$

What is the probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month?

This is 1 subtracted by the pvalue of Z when X = 2260.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{2260 - 2350}{32.249}$

Z = -2.79

Z = -2.79 has a pvalue of 0.0026

1 - 0.0026 = 0.9974

0.9974 = 99.74% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month.

answered: Guest

step-by-step explanation:

answered: Guest

any options?

step-by-step explanation:

Abox has a length of 6 centimeters a width of 4 centimeters and a height of 5 centimeters jen filled

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 15:00, Shavaila18

The data shown in the table below represents the weight, in pounds, of a little girl, recorded each year on her birthday. age (in years) weight (in pounds) 2 32 6 47 7 51 4 40 5 43 3 38 8 60 1 23 part a: create a scatter plot to represent the data shown above. sketch the line of best fit. label at least three specific points on the graph that the line passes through. also include the correct labels on the x-axis and y-axis. part b: algebraically write the equation of the best fit line in slope-intercept form. include all of your calculations in your final answer. part c: use the equation for the line of best fit to approximate the weight of the little girl at an age of 14 years old.

Answers: 3

continue

Mathematics, 21.06.2019 15:00, dward5823

Write a corresponding real world problem to represent 2x - 125=400

Answers: 1

continue

Mathematics, 21.06.2019 16:00, nathanb29oue8gj

Aheated piece of metal cools according to the function c(x) = (.5)x ? 7, where x is measured in hours. a device is added that aids in cooling according to the function h(x) = ? x ? 2. what will be the temperature of the metal after two hours?

Answers: 2

continue

Mathematics, 21.06.2019 16:00, anthonyjackson12aj

What are the measures of ∠a, ∠b, ∠c and ∠d? explain how to find each of the angle measure.

Answers: 1

continue

Do you know the correct answer?

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a m...