Question Six

a) A random sample of n = 100 frames of 100mm x 50mm was selected from a consignment of 500 frames. When their depth was measured it was found that the mean was 106mm and standard deviation was 3.5mm. Construct a 90% confidence interval estimate of the mean depth of all the frame in the entire consignment.

Part (a) is relatively straight forward.there are 4 aces in a standard 52-card deck. so the probability that an ace is picked is just 4/52.part (b): note that there are 4 suits in a standard 52-card deck. so picking hearts will be 13/52 or 1/4.part (c): the probability condition or means we need to add the two probabilities because we do not want them simultaneously. so, we end up getting pr(ace) + pr(heart).from part (a), we found that picking an ace had a probability of 4/52, which is reduced down to 1/13.from part (b), we found that picking a heart had a probability of 1/4.so, the probability of an ace or a heart is 1/13 + 1/4 = 4/52 + 13/52 = 17/52.

Answer(d); when the future events will possibly occur and the amount can be reasonably estimated;