In a contest, a participant is blindfolded and then he is asked to put a very thin sticker on a straight line on a wall. Let X be the distance in cm they place the sticker from the center of the line. Assume that X follows normal distribution with mean 0 and variance 100. (A positive value for X means they miss the target to the right and a negative value that they miss the target to the left) (a) Find the probability that the participant puts the sticker on the center. (b) Find the probability that the participant puts the sticker within 3cm of the center. (c) If the participant wins 20 points if they puts the sticker in the center, 15 points if they put the sticker within 3cm of the center, 10 points if they put the sticker between 3cm and 10cm away from the center, 5 points if they put the sticker between 10cm and 20cm away from the center and 0 points otherwise. Find the expected number of points that the participant will win.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In a contest, a participant is blindfolded and then he is asked to put a very thin sticker on a straight line on a wall. Let X be the distance in cm they place the sticker from the center of the line. Assume that X follows
miss the target to the left)
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(a) Find the
probability that the participant puts the sticker on the center. -
(b) Find the probability that the participant puts the sticker within 3cm of the center.
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(c) If the participant wins 20 points if they puts the sticker in the center, 15 points if they put the sticker within 3cm of the center, 10 points if they put the sticker between 3cm and 10cm away from the center, 5 points if they put the sticker between 10cm and 20cm away from the center and 0 points otherwise. Find the expected number of points that the participant will win.
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