Suppose you are given a multiple-choice test with 10 questions, each with 4 answer choices. If you randomly guess the answer to each question, what is the probability that you answer at least 7 questions correctly? Additionally, what is the expected number of questions that you would answer correctly by guessing, and what is the standard deviation of the number of questions answered correctly?

Suppose the probability of success is p=31%p=31%. What is the probability of 77 successes in 88 trials?

A consulting firm advises on sampling and statistical procedures that can be used by their clients to control their manufacturing processes. A sample of a dimension existing 800 data points was collected from the process during a time that it was operating successfully. The sample standard deviation was .21 and since the number of samples was so large this was considered to be the population standard deviation. The consulting firm then suggested that data be collected in groups of 30 to periodically monitor and correct the process. The design specification was determined to be 12. The hypothesis test suggested by the consulting firm was:                                                                         Ho: μ = 12                                                                               H1: μ ≠ 12        Corrective action will be taken whenever Ho is rejected.                  Sample 1         Sample 2         Sample 3             11.55               11.62               11.91…

A population proportion is 0.5. Suppose a random sample of 658 items is sampled randomly from this population.   what is the probability that the sample proportion is between 0.53 and 0.56? What is the probability that the sample proportion is less than 0.49?