A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 30 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 6% rate of defects? (Report answer as a decimal value accurate to four decimal places.) P(accept shipment) =

BlueSky Air has the best on-time arrival rate with 75% of its flights arriving on time. A test is conducted by randomly selecting 15 BlueSky Air flights and observing whether they arrive on time. What is the probability that two flights of BlueSky Air arrive late? (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). Probability (as a proportion)

The Census Bureau gives this distribution for the number of people in American households in 2016. Family size 1 2 4 6. 7 Proportion 0.28 0.35 0.15 0.13 0.06 0.02 0.01 Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7. Suppose you take a random sample of 4000 American households. About how many of these households will be of size 2? Sizes 3 to 7? The number of households of size 2 is about The number of households of size 3 to 7 is about

When practicing basketball, Rachel has a 67% chance of making a free throw. She shoots 12 free throws. Let the random variable X be the number of free throws she makes. Find the probability she makes exactly 5 free throws. Give your answer to at least three nonzero decimal places. What is the expected value of X. Interpret this value.