Mathematics, 05.05.2020 13:22 ValerieRubyPena

Add a cell phone assembly plant, 80% of the cell phone keypad pass inspection. A random sample of 181 keypads is analyzed. Find the probability that less than 76 in the sample keypads pass inspection.

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Answer from: doritasanchez

0% probability that less than 76 in the sample keypads pass inspection.

Step-by-step explanation:

I am going to use the normal approximation to the binomial 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 problem, we have that:

n = 181, p = 0.8

$\mu = E(X) = np = 181*0.8 = 144.8$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{181*0.8*0.2} = 5.38$

Find the probability that less than 76 in the sample keypads pass inspection.

Using continuity correction, this is P(X < 76 - 0.5) = P(X < 75.5) , which is the pvalue of Z when X = 75.5.

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

$Z = \frac{75.5 - 144.8}{5.38}$

Z = -12.88

Z = -12.88 has a pvalue of 0

0% probability that less than 76 in the sample keypads pass inspection.

Answer from: Quest

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

Answer from: Quest

Hello sorry can’t good luck tho