Packets of biscuits are produced by a machine. The weights X, in grams, of packets of biscuits can be modelled by a normal distribution where X~ N(u, oʻ). A packet of biscuits is
considered to be underweight if it weighs less than 250 grams.
(a) Given that u = 253 and o=1.5 find the probability that a randomly chosen packet of
biscuits is underweight.
The manufacturer makes the decision that the probability that a packet is underweight should
be 0.002. To do this u is increased and o remains unchanged.
(b)
Calculate the new value of u giving your answer correct to two decimal places.
The manufacturer is happy with the decision that the probability that a packet is underweight
should be 0.002, but is unhappy with the way in which this was achieved. The machine is
now adjusted to reduce o and return u to 253.
(c)
Calculate the new value of o.

Me on this one i will give you 20pts. answer should be in detail . this is the discussion topic. one of the most fiercely debated topics in sports is the hot hand theory. the hot hand theory says that success breeds success. in other words, rather than each shot a basketball player takes or each at-bat a baseball player has being an independent event, the outcome of one event affects the next event. that is, a player can get hot and make a lot of shots in a row or get a lot of hits in a row. the hot hand theory, however, has been shown to be false in numerous academic studies. read this article, which discusses the hot hand theory as it relates to a professional basketball player. state whether you agree or disagree with the hot hand theory, and give reasons for your opinion. be sure to use some of the terms you’ve learned in this unit, such as independent event, dependent event, and conditional probability, in your answer.