MATHEMATICS COLLEGE

A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that it has contracted, find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.

Answers

Answer 1

Answer:

Answer:

68.26% probability that the number of jobs finished on time is within 1 standard deviation of the mean.

Step-by-step explanation:

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:

$Z = (X - \mu)/(\sigma)$

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.

Looking at a random sample of 8 jobs that it has contracted, find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.

Within 1 standard deviation of the mean is from Z = -1 to Z = 1. So this probability is the pvalue of Z = 1 subtracted by the pvalue of Z = -1.

Z = 1 has a pvalue of 0.8413

Z = -1 has a pvalue of 0.1587

So there is a 0.8413 - 0.1587 = 0.6826 = 68.26% probability that the number of jobs finished on time is within 1 standard deviation of the mean.

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From the records of a health-insurance companies in Pennsylvania, it is known that 58% of the accounts include dental coverage. A researcher would like to take a random sample of 500 accounts to review. Find the standard deviation of the sample proportion in this situation. Give your answer to 4 decimal places. For help on how to input a numeric answer, please see "Instructions for inputting a numeric response."

Answers

Answer: 0.0221

Step-by-step explanation:

We know that the formula to find the standard deviation of the sample proportion is :

$\sigma_p=\sqrt{(p(1-p))/(n)}$

, where p = proportion of success.

n= sample size.

As per given , we have

p=0.58

n= 500

Then, the standard deviation of the sample proportion in this situation would be :

$\sigma_p=\sqrt{(0.58(1-0.58))/(500)}\n\n=\sqrt{(0.2436)/(500)}\n\n=√(0.0004872)\n\n\approx0.0221$

Hence, the standard deviation of the sample proportion in this situation is 0.0221 .

Multiply the conjugates.(x + 2y)(x - 2y)

First to give correct answer gets the brainliest, and hurry please this is timed

Answers

Answer;

equal; $x^(2) - 4y^(2)$

When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is called ______________.

Answers

Answer:

Cross section

Step-by-step explanation:

Cross section refers to the new two dimensional face exposed when we slice through a three dimensional objects.

It can also be the surface or shape exposed by making a straight cut through something, especially at right angles to an axis.

Cross section is the plane surface(two-dimensional objects) formed by cutting across a solid shape (three-dimensional shape) especially perpendicular to its longest axis.

The computer that controls a bank's automatic teller machine crashes a mean of 0.5 times per day. What is the probability that, in any seven-day week, the computer will crash less than 3 times? Round your answer to four decimal places.

Answers

Answer:

0.3216 = 32.16% probability that, in any seven-day week, the computer will crash less than 3 times

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval

Mean of 0.5

7-day week, so $\mu = 7*0.5 = 3.5$

What is the probability that, in any seven-day week, the computer will crash less than 3 times?

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 0) = (e^(-3.5)*(3.5)^(0))/((0)!) = 0.0302$

$P(X = 1) = (e^(-3.5)*(3.5)^(1))/((1)!) = 0.1057$

$P(X = 2) = (e^(-3.5)*(3.5)^(2))/((2)!) = 0.1850$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0302 + 0.1057 + 0.1857 = 0.3216$

0.3216 = 32.16% probability that, in any seven-day week, the computer will crash less than 3 times

Final answer:

To find the probability that the computer will crash less than 3 times in a seven-day week, we can use the binomial probability formula.

Explanation:

To find the probability that the computer will crash less than 3 times in a seven-day week, we can use the binomial probability formula. The formula for binomial probability is:

$P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)$

Where:

P(X = k) is the probability of exactly k successes
C(n, k) is the combination function for choosing k items from a set of n
p is the probability of success for each individual trial
n is the number of trials

In this case, the mean number of crashes per day is 0.5, which means the probability of a crash in a single day is 0.5. Since we're interested in the probability of less than 3 crashes in a seven-day week, we can calculate P(X < 3) using the binomial probability formula with n = 7, p = 0.5, and k = 0, 1, 2:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial probability formula, we can calculate:

$P(X = 0) = C(7, 0) * 0.5^0 * (1-0.5)^(^7^-^0)\nP(X = 1) = C(7, 1) * 0.5^1 * (1-0.5)^(^7^-^1)\nP(X = 2) = C(7, 2) * 0.5^2 * (1-0.5)^(^7^-^2)$