Mathematics, 30.03.2020 19:03, wetogether0123

The average cost of a one-bedroom apartment in a town is $650 per month. What is the probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $630 if the population standard deviation is $100?

Answers: 3

Show answers

Answers

Probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $630 is 0.0793.

Step-by-step explanation:

We are given that the average cost of a one-bedroom apartment in a town is $650 per month. Assume the population standard deviation is $100.

Also, a sample of 50 one-bedroom apartments is selected.

Let $\bar X$ = sample mean cost

The z-score probability distribution for sample mean is given by ;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population average cost = $650

$\sigma$ = population standard deviation = $100

n = sample of one-bedroom apartments = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, the probability that the sample mean is less than $630 is given by = P( $\bar X$ < $630)

P( $\bar X$ < $630) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{630 - 650}{\frac{100}{\sqrt{50} } }$ ) = P(Z < -1.41) = 1 - P(Z $\leq$ 1.41)

= 1 - 0.9207 = 0.0793

The above probability is calculated using z table by looking at value of x = 1.41 in the z table which have an area of 0.92073.

Therefore, probability that the sample mean is less than $630 is 0.0793.

answered: dnee8321

We can use standard normal variate and use z tables to find the needed probability.

The needed probability is 0.0793

Given that:The average cost of one bedroom apartment = $\mu = \$650$ The standard deviation of population = $\sigma = \$ 100$ The size of the sample = n = 50

The mean of sample is needed to be less than $630

Let the sample mean be tracked by random variable $\overline{X}$

Transforming $\overline{X}$ to standard normal variate:

Since standard deviation is known already, we can transform the r.v. approximately into standard normal variate by:

$Z = \dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\$

Then we will have:

$P(\overline{X} < 630) = P(Z < \dfrac{630 - 650}{\dfrac{100}{\sqrt{50}}} ) = P(Z < -\sqrt{2})\\\\P(\overline{X} < 630) = P(Z < -1.41) = 1 - P(Z \leq 1.41) = 1 - 0.9207 = 0.0793$

The value 0.9207 is p value for z-score 1.41 seen from the z-score table.

Thus, the needed probability is 0.0793

Learn more about z-score here:

answered: Guest

step-by-step explanation:

Which expression is equivalent to 24 1/3

answered: Guest

50- 250 is correct i did that one too

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 20:30, ultimatesaiyan

Answer asap ill give ! ’ a sample of radioactive material decays over time. the number of grams, y , of the material remaining x days after the sample is discovered is given by the equation y = 10(0.5)^x. what does the number 10 represents in the equation? a. the half-life of the radioactive material, in days b. the amount of the sample, in grams, that decays each day c. the time, in days, it will take for the samples to decay completely d. the size of the sample, in grams, at the time the material was discovered

Answers: 1

continue

Mathematics, 21.06.2019 20:30, heyyyyy39

The cost for an uberi is $2.50 plus $2.00 mile. if the total for the uber ride was $32.50, how many miles did the customer travel?

Answers: 3

continue

Mathematics, 22.06.2019 04:00, lulabelles7750

Brad earns $12.75/hr and works 40 hours a week. what is his gross annual income?

Answers: 1

continue

Mathematics, 22.06.2019 04:30, sindy35111

Megan and desmond each add the same amount of water to their aquarium megan makes 5 ml of chemical solution with every gallon of water for her aquarium desmond mixed 8 ml of chemical solution for every 2 gallon of the water for his aquarium.

Answers: 3

continue

Do you know the correct answer?

The average cost of a one-bedroom apartment in a town is $650 per month. What is the probability of...