Mathematics, 30.10.2020 17:40 jessicagustama

A survey of all medium- and large-sized corporations showed that of them offer retirement plans to their employees. Let be the proportion in a random sample of such corporations that offer retirement plans to their employees. Find the probability that the value of will be greater than .

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Answer from: andrea1704

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$P(0.51 < \^ p < 0.61 ) = 0.2587$

$P(\^ p 0.71 ) = 0.15165$

Step-by-step explanation:

From the question we are told that

The population proportion is p = 0.64

The sample size is n = 50

Generally the mean of this sampling distribution is

$\mu_{x} = p = 0.64$

Generally the standard deviation is mathematically represented as

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

=> $\sigma = \sqrt{ \frac{0.64(1- 0.64 )}{ 50} }$

=> $\sigma = 0.068$

Generally the probability that the value of $\^ p$ will be between 0.54 and 0.61 is mathematically represented as

$P(0.51 < \^ p < 0.61 ) = P( \frac{0.5 4 - \mu_{x}}{\sigma } < \frac{\^ p- \mu_{x}}{\sigma } < \frac{0.6 1 - \mu_{x}}{\sigma } )$

$\frac{\^ p -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \^ p )$

$P(0.51 < \^ p < 0.61 ) = P( \frac{0.5 4 - 0.64}{0.068 } < Z < \frac{0.6 1 - 0.64}{0.068} )$

$P(0.51 < \^ p < 0.61 ) = P(-1.470 < Z < -0.4412 )$

=> $P(0.51 < \^ p < 0.61 ) = P( Z < -0.4412 ) - P(Z < -1.470 )$

From the z table the probabilities of ( Z < -0.4412 ) and (Z < -1.912 ) is

P ( Z < -0.4412 ) = 0.32953

and

P(Z < -1.470 ) = 0.070781

Generally

$P(0.51 < \^ p < 0.61 ) = 0.32953 -0.070781$

$P(0.51 < \^ p < 0.61 ) = 0.2587$

Generally the probability that the value of $\^ p$ will be greater than 0.71 is mathematically represented as

$P(\^ p 0.71 ) = P( \frac{\^ p - \mu_{x}}{\sigma} \frac{0.71 - 0.64 }{ 0.068 } )$

=> $P(\^ p 0.71 ) = P( Z 1.0294 )$

From the z table the probabilities of ( Z > 1.0294 )

P( Z 1.0294 ) = 0.15165

$P(\^ p 0.71 ) = 0.15165$

A survey of all medium- and large-sized corporations showed that of them offer retirement plans to t

Answer from: Quest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

Answer from: Quest

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction