A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 12,441 children. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 12,441 children. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 12,441 children is 0 or 1. What is the probability of more than one case? Does the cluster of four cases appear to be attributable to random chance? Why or why not?
A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 12,441 children. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 12,441 children. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 12,441 children is 0 or 1. What is the probability of more than one case? Does the cluster of four cases appear to be attributable to random chance? Why or why not?
A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 12,441 children. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 12,441 children. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 12,441 children is 0 or 1. What is the probability of more than one case? Does the cluster of four cases appear to be attributable to random chance? Why or why not?
A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 12,441 children.
Assuming that this tumor occurs as usual, find the mean number of cases in groups of
12,441 children.
Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 12,441 children is 0 or 1.
What is the probability of more than one case?
Does the cluster of four cases appear to be attributable to random chance? Why or why not?
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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