Mathematics, 08.04.2020 04:33 stgitskaysie367

At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. A random sample of 111 keypads is analyzed. Find the probability that the proportion of the sample keypads that pass inspection is between 0.72 and 0.8. Round your answer to four decimal places and please explain how you came up with the answer.

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Using the normal distribution and the central limit theorem, it is found that there is a 0.6677 = 66.77% probability that the proportion of the sample keypads that pass inspection is between 0.72 and 0.8.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample proportions of a proportion p in a sample of size n has mean $\mu = p$ and standard error $s = \sqrt{\frac{p(1 - p)}{n}}$ .

In this problem:

77% of the cell phone keypads pass inspection, hence

.A random sample of 111 keypads is analyzed, hence n = 111

The mean and the standard error are given by:

$\mu = p = 0.77$

$s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.77(0.23)}{111}} = 0.0399$

The probability is the p-value of Z when X = 0.8 subtracted by the p-value of Z when X = 0.72.

X = 0.8:

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

By the Central Limit Theorem

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

$Z = \frac{0.8 - 0.77}{0.0399}$

Z = 0.75

Z = 0.75 has a p-value of 0.7734.

X = 0.72:

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

$Z = \frac{0.72 - 0.77}{0.0399}$

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

0.7734 - 0.1057 = 0.6677

0.6677 = 66.77% probability that the proportion of the sample keypads that pass inspection is between 0.72 and 0.8.

For more on the normal distribution and the central limit theorem, you can check link

Answer from: caymanbecs

The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

Let p = the proportion of keypads that pass inspection at a cell phone assembly plant.

The probability that a randomly selected cell phone keypad passes the inspection is, p = 0.77.

A random sample of n = 111 keypads is analyzed.

Then the sampling distribution of $\hat p$ is:

$\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})\\\Rightarrow \hat p\sim N (0.77, 0.04)$

Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:

P(0.72

=P(-1.25

Thus, the probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

Answer from: Quest

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.