A population proportion is 0.70. A sample of size 100 will be taken and the sample proportion  p  will be used to estimate the population proportion. (Round your answers to four decimal places.) (a) What is the probability that the sample proportion will be within ±0.03 of the population proportion?   (b) What is the probability that the sample proportion will be within ±0.05 of the population proportion?

In looking at the results of a standardized exam, 72% of those taking the test choose the correct answer on the first question. Answer the following for 400 test takers who are to be randomly chosen. After taking the sample and administering the test, 320 of the test takers answer the first question correctly.   The sample proportion is ____________________.         Find the mean and variance for the distribution of sample proportions from samples of size n = 400.   Mean: __________________       Variance: ___________________                 The probability is ____________________ for taking another random sample of size n = 400 test takers and more than 75% of them getting the correct answer on this question.

Find the probability P(not E) if P(E)= 0.38. The probability P(hot E) is (Simplify your answer.)

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The Law of Large Numbers states that as the number of observations in a sample increases, the mean of this is sample becomes a. exactly equal to the mean. b. closer and closer to the population mean. c. close to 0. d. further and further from the population mean.

Need help with this probability question.

Toss five fair coins and let x equal the number of heads observed. a. Identify the sample points associated with this experiment, and assign a value of x to each sample point. Then list all the possible values of x. b. Calculate p(x) for the values x = 1 and x = 2. c. Construct a probability histogram for p(x). d. What is P(x = 1 or x = 4)?