Mathematics, 18.06.2020 15:57 cramirezorozco392

Consider the probability that at least 91 out of 155 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 59%.Approximate the probability using the normal distribution. Round your answer to four decimal places.

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Answer from: vieraml58

0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.

Step-by-step explanation:

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:

n = 155, p = 0.59

$\mu = E(X) = np = 155*0.59 = 91.45$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{155*0.59*0.41} = 6.12$

Probability that at least 91 out of 155 students will pass their college placement exams.

Using continuity correction, this is $P(X \geq 91 - 0.5) = P(X \geq 90.5)$ , which is 1 subtracted by the pvalue of Z when X = 90.5. So

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

$Z = \frac{90.5 - 91.45}{6.12}$

Z = -0.155

Z = -0.155 has a pvalue of 0.4384

1 - 0.4384 = 0.5616

0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.

Answer from: Quest

its 0.1 miles per minute

Plz i’ve been on this pretest for weeks!

Answer from: Quest

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.
Which table shows a proportional relationship between x and y

Which table shows a proportional relationship between x and y

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