In a hamster breeder's experience the number X of live pups in a litter of a female not over twelve months in age who has not borne a litter in the past six weeks has the probability distribution x 3 4 5 6 7 8 9 P(x) 0.4 0.10 0.26 0.31 0.22 0.05 0.02 Find the probability that the next litter will produce five to seven live pups. Find the probability that the next litter will produce at least six live pups. Compute the mean and standard deviation of X. Interpret the mean in the context of the problem.
In a hamster breeder's experience the number X of live pups in a litter of a female not over twelve months in age who has not borne a litter in the past six weeks has the probability distribution x 3 4 5 6 7 8 9 P(x) 0.4 0.10 0.26 0.31 0.22 0.05 0.02 Find the probability that the next litter will produce five to seven live pups. Find the probability that the next litter will produce at least six live pups. Compute the mean and standard deviation of X. Interpret the mean in the context of the problem.
In a hamster breeder's experience the number X of live pups in a litter of a female not over twelve months in age who has not borne a litter in the past six weeks has the probability distribution x 3 4 5 6 7 8 9 P(x) 0.4 0.10 0.26 0.31 0.22 0.05 0.02 Find the probability that the next litter will produce five to seven live pups. Find the probability that the next litter will produce at least six live pups. Compute the mean and standard deviation of X. Interpret the mean in the context of the problem.
In a hamster breeder's experience the number X of live pups in a litter of a female not over twelve months in age who has not borne a litter in the past six weeks has the probability distribution
x
3
4
5
6
7
8
9
P(x)
0.4
0.10
0.26
0.31
0.22
0.05
0.02
Find the probability that the next litter will produce five to seven live pups.
Find the probability that the next litter will produce at least six live pups.
Compute the mean and standard deviation of X. Interpret the mean in the context of the problem.
Transcribed Image Text:6. In a hamster breeder's experience the number X of live pups in a litter of a female not over
twelve months in age who has not borne a litter in the past six weeks has the probability
distribution
4
7
8
9
P(x)
0.4
0.10
0.26
0.31
0.22
0.05
0.02
a. Find the probability that the next litter will produce five to seven live pups.
b. Find the probability that the next litter will produce at least six live pups.
c. Compute the mean and standard deviation of X. Interpret the mean in the context of the
problem.
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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