The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs. a) About what proportion of Mets home runs have length between 390 and 400 feet? b) About what proportion of Mets home runs have length greater than 410 feet? c) About how many of the 81 sampled home runs have length less than 380 feet? (nearest integer)
The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs. a) About what proportion of Mets home runs have length between 390 and 400 feet? b) About what proportion of Mets home runs have length greater than 410 feet? c) About how many of the 81 sampled home runs have length less than 380 feet? (nearest integer)
The lengths of home runs hit by players for the Mets have approximately a normal distribution with μ = 399 feet and a standard deviation of σ=31.16 feet. Suppose that we randomly select 81 home runs hit by players of the Mets. Let X be the random variable representing the mean length of home runs in feet and let Xtot be the random variable representing the sum of the lengths of the home runs in feet for the 81 selected home runs.
a) About what proportion of Mets home runs have length between 390 and 400 feet?
b) About what proportion of Mets home runs have length greater than 410 feet?
c) About how many of the 81 sampled home runs have length less than 380 feet? (nearest integer)
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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