a) Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to

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a) Assume that a sample is used to estimate a populationproportion p. Find the margin oferror M.E. that corresponds to a sample of size140 with 44.3% successes at a confidence level of 80%.M.E. = %Answer should be obtained without any preliminary rounding.However, the critical value may be rounded to 3 decimal places.Round final answer to one decimal place
b) Giving a test to a group of students, the grades andgender are summarized below
Let pp represent the percentage of all male students whowould receive a grade of B on this test. Use a 85% confidenceinterval to estimate p to three decimal places.Enter your answer as a tri-linear inequality using decimals (notpercents).
c) You want to obtain a sample to estimate the proportionin the population who support gun control. Based on previousevidence, you believe the population proportion isapproximately 24%. You would like to be 99% confident thatyour estimate is within 2% of the true population proportion. Howlarge of a sample size is required?Do not round mid-calculation. However, use a critical valueaccurate to three decimal places.
d)
An environmental science teacher at a high school with a largepopulation of students wanted to estimate the proportion ofstudents at the school who regularly recycle plastic bottles. Theteacher selected a random sample of students and was asked torespond yes or no to the following question:
Do you regularly recycle plastic bottles?
Based on the responses, a 90 percent confidence interval for theproportion of all students at the school who would respond yes tothe question was calculated with a margin of error of± 3.5%.
How many students were in the sample selected by theenvironmental science teacher?
e) Based on historical data, your manager believes that 29%of the company's orders come from first-time customers. A randomsample of 200 orders will be used to estimate the proportion offirst-time-customers. What is the probability that the sampleproportion is less than 0.3?Answer = (Enter your answer as a number accurate to 4decimal places.)
f)
Express the confidenceinterval 82.7%<p<91.7%82.7%<p<91.7% in theform of ˆp±MEp^±ME.% ±± %
Hint: Find the mid-point of the interval tofind ˆpp^.