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2.According to www.city-data, the mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know t

igor_vitrenko [27]

Answer:

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.

This means that $\mu = 192723, \sigma = 42000$

Sample of 75:

This means that $n = 75, s = \frac{42000}{\sqrt{75}}$

What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?

1 subtracted by the p-value of Z when X = 190000. So

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

By the Central Limit Theorem

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

$Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}$

$Z = -0.56$

$Z = -0.56$ has a p-value of 0.2877

1 - 0.2877 = 0.7123

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

5 0

3 years ago

A student is trying to solve the system of two equations given below:

Shkiper50 [21]

Answer:

B

Step-by-step explanation:

eliminating the y-term

(y + z = 6) × -5

6 0

3 years ago

In an area of Russia records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per

skelet666 [1.2K]

Answer:

Option d.

Step-by-step explanation:

The equation of the line of least squares is given as

$\hat{y} = -9.12+ 4.38x$

where $\hat{y}$ is the yield of wheat (bushels per acre) and x is the rainfall (in inches).

We need to find the expected number of inches of rain if the yield is 60 bushels of wheat per acre.

Substitute $\hat{y}=60$ in the given equation.

$60= -9.12+ 4.38x$

Add 9.12 on both sides.

$60+9.12=4.38x$

$69.12=4.38x$

Divide both sides by 4.38.

$\frac{69.12}{4.38}=x$

$x\approx 15.78$

The expected number of inches of rain is 15.78.

Therefore, the correct option is d.

3 0

3 years ago

What is the measure of angle x? Enter your answer in the box. m∠x= °

faltersainse [42]

Answer:

61

Step-by-step explanation:

The sum of all the angles in any triangle is 180.

To find x, just add the other two angles and subtract the sum from 180.

37 + 82 = 119

180 - 119 = 61.

Therefore, the answer is 61 degrees.

6 0

3 years ago

Read 2 more answers

You are running a race. The probability that you win is 3/5. What is the probability that you lose at most 2 out of your 6 races

Veronika [31]

Answer:

The probability that you lose at most 2 out of your 6 races is 0.54432.

Step-by-step explanation:

We are given that you are running a race. The probability that you win is 3/5.

There are total of 6 races.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 races

r = number of success = at most 2 lost

p = probability of success which in our question is probability that

you lose a race = 1 - (3/5) = 2/5 or 0.4

Let X = Number of races lost

So, X ~ Binom(n = 6, p = 0.40)

Now, the probability that you lose at most 2 out of your 6 races is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}$

= $1 \times1 \times 0.60^{6} + 6 \times 0.40^{1} \times 0.60^{5} +15\times 0.40^{2} \times 0.60^{4}$

= 0.54432

7 0

3 years ago