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.
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.
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.
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.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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