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

Hi! mark me brainliest if i : )y = 0.213x – 352.0 represents this linear model shown in the data table.plug in the values of x into the equation for a double check.let's try 1980.y = 0.213(1980) – 352.0y = 69.74which is closest to the 70.1 whereas other options do not satisfy the condition.

Answer from: Quest

mx+89b(-98)nb

step-by-step explanation:

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