Mathematics, 31.03.2020 00:43 haleyscales825

Consider the probability that more than 91 out of 149 DVDs will work correctly. Assume the probability that a given DVD will work correctly is 66%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

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Answer from: trishinada63

0.8810 = 88.10% probability that more than 91 out of 149 DVDs will work correctly.

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 = 149, p = 0.66

$\mu = E(X) = np = 149*0.66 = 98.34$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{149*0.66*0.34} = 5.78$

Consider the probability that more than 91 out of 149 DVDs will work correctly.

Using continuity correction, this is P(X > 91 + 0.5 = 91.5), which is one subtracted by the pvalue of Z when X = 91.5. So

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

$Z = \frac{91.5 - 98.34}{5.78}$

Z = -1.18

Z = -1.18 has a pvalue of 0.1190

1 - 0.1190 = 0.8810

0.8810 = 88.10% probability that more than 91 out of 149 DVDs will work correctly.

Answer from: Quest

answer: the anser is 3

step-by-step explanation:

c- 2o is equal to 9

Answer from: Quest

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did not satisfy the given simplify expression.

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Consider the probability that more than 91 out of 149 DVDs will work correctly. Assume the probabili...