Mathematics, 29.05.2020 14:57 clmorcutt420

Suppose 30% of a population possess a given characteristic. If a random sample of size 1200 is drawn from the population, then the probability that less than 348 possess that characteristic is

Answers: 1

Show answers

Answers

Answer from: orlando19882000

The population follows a normal distribution.

The probability that less than 348 possess that characteristic is 0.2248

The given parameters are:

$\mathbf{n = 1200}$

$\mathbf{p = 30\%}$

Start by calculating the mean:

$\mathbf{\mu =np}$

$\mathbf{\mu =1200 \times 30\%}$

$\mathbf{\mu =360}$

Calculate the standard deviation

$\mathbf{\sigma = \sqrt{np(1 - p)}}$

$\mathbf{\sigma = \sqrt{360(1 - 30\%)}}$

$\mathbf{\sigma = \sqrt{252}}$

$\mathbf{\sigma = 15.87}$

Calculate the z-score

$\mathbf{z = \frac{x - \mu}{\sigma}}$

Where:

x = 348

So, we have:

$\mathbf{z = \frac{348 - 360}{15.87}}$

$\mathbf{z = -\frac{12}{15.87}}$

$\mathbf{z = -0.7561}$

So, the probability is represented as:

$\mathbf{P(x < 348) = P(z < -0.7561)}$

From the z-table of probabilities, we have:

$\mathbf{P(x < 348) = 0.2248}$

Hence, the probability that less than 348 possess that characteristic is 0.2248

Read more about probabilities at:

link

Answer from: DanteMadrid33

The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.

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 question, we have that:

n = 1200, p = 0.3

$\mu = E(X) = np = 1200*0.3 = 360$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.3*0.7} = 15.8745$

The probability that less than 348 possess that characteristic is

Using continuity correction, this is P(X < 348 - 0.5) = P(X < 347.5), which is the pvalue of Z when X = 347.5. So

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

$Z = \frac{347.5 - 360}{15.8745}$

Z = -0.79

Z = -0.79 has a pvalue of 0.2148.

The probability that less than 348 possess that characteristic is 0.2148 = 21.48%.

Answer from: Quest

Best answer that i found on yahoo ok set : x= length of 2nd piece in cm x- 3= length of 1st piece in cm x-4= length of 3rd piece in cm then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20 3x - 7= 20 3x= 27 x= 9 the shortest piece is the third piece which is x- 4 x-4 9-4 = 5 the length of the smallest piece is 5 cm. the other lengths are 9 cm 6 cm

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:00

What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)

Answers: 3

Answer

Mathematics, 22.06.2019 00:00

Which of these angles are supplementary? a. 100o and 90o b. 78o and 102o c. 54o and 146o d. 12o and 78o

Answers: 1

Answer

Mathematics, 22.06.2019 00:20

❤️ (geometry) does the construction demonstrate how to copy an angle correctly using technology a) yes; the distance between points a and f was used to create circle h b) yes; the distance between points f and g was used to create circle h c)no; the distance between points a and f was used to create circle h d) no; the distance between points f and g was used to create circle h

Answers: 2

Answer

Mathematics, 22.06.2019 02:30

The price of a visit to the dentist is \$50$50. if the dentist fills any cavities, an additional charge of \$100$100 per cavity gets added to the bill. if the dentist finds nn cavities, what will the cost of the visit be?

Answers: 2

Answer

You know the right answer?

Suppose 30% of a population possess a given characteristic. If a random sample of size 1200 is drawn...

Questions