Answered

Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.

suppose a large shipment of laser printers contained 14% defectives. if a sample of size 411 is selected, what is the probability that the sample proportion will differ from the population proportion by greater than 4%? round your answer to four decimal places.

Sagot :

Varshamittal029idn

The probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990.

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:

µ = p

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

σ = √p(1-p)/n

The information provided is:

p = 0.14

n = 41

As the sample size is large, i.e n = 411 > 30. the central limit theorem can be used to approximate the sampling distribution of sampling proportion.

Compute the values of P(p^ - p >0.04) as follows:

P(p^ - p < 0.04) = P(p^-p/σ > 0.04/√0.14(1-0.14)/411

= P(Z>2.33)

= 0.990

Thus the probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990

Learn more about Normal distribution here:

brainly.com/question/25638875

#SPJ4

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.