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.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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