Mathematics, 26.03.2020 19:35 sulemmaa

A group of realtors estimates that 23% of all homes purchased last year were considered investment properties.
If a sample of 800 homes sold last year is obtained, what is the probability that at most 200 homes are going to used as investment property?

Answers: 3

Show answers

Answers

Answer from: pmgpmgutube

90.99% probability that at most 200 homes are going to used as investment property

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

p = 0.23, n = 800

$\mu = E(X) = np = 800*0.23 = 184$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.23*0.77} = 11.90$

If a sample of 800 homes sold last year is obtained, what is the probability that at most 200 homes are going to used as investment property?

This is the pvalue of Z when X = 200. So

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

$Z = \frac{200 - 184}{11.90}$

Z = 1.34

Z = 1.34 has a pvalue of 0.9099

90.99% probability that at most 200 homes are going to used as investment property

Answer from: Quest

ryan had a head start of 10 meters.

Answer from: Quest

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

$m\angle qrt=156^o$

$m\angle qst=156^o$

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

Another question on Mathematics

Mathematics, 21.06.2019 15:30

Match each equation with the operation you can use to solve for the variable. subtract 10. divide by 10. divide by 5. subtract 18. multiply by 10. add 18. add 10. multiply by 5. 5 = 10p arrowright p + 10 = 18 arrowright p + 18 = 5 arrowright 5p = 10 arrowright

Answers: 3

Answer

Mathematics, 21.06.2019 18:00

Find the perimeter of the figure shown above. a. 40 cm c. 52 cm b. 60 cm d. 75 cm select the best answer from the choices provided

Answers: 1

Answer

Mathematics, 21.06.2019 21:50

Tamar is measuring the sides and angles of tuv to determine whether it is congruent to the triangle below. which pair of measurements would eliminate the possibility that the triangles are congruent

Answers: 1

Answer

Mathematics, 21.06.2019 22:20

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)

Answers: 2

Answer

You know the right answer?

A group of realtors estimates that 23% of all homes purchased last year were considered investment p...

Questions

Mathematics, 19.12.2020 01:00

What is the slope of the equation of a line that passes through the points?

Mathematics, 19.12.2020 01:00

Condense the logarithm r log d + x log q...

Mathematics, 19.12.2020 01:00

If r = 1 and 0(with a slash through it) = 4π/3 what is the approximate arc length...