Consider babies born in the "normal" range of 37-43 weeks gestational age.Extensive data supports the assumption that for such babies born in the United States,birth weight is normally distributed with mean 3432 g and standard deviation 482 g.[The article "Are Babies Normal?" (The American Statistician, 1999:298-302) analyzed data from a particular year;for a sensible choice of class intervals,a histogram did not look at all normal,but after further investigations it was determined that this was due to some hospitals measuring weight in grams and others measuring to the nearest ounce and then converting to grams. A modified choice of class intervals that allowed for this gave a histogram that was well described by a normal distribution.) a. What is the probability that the birth weight of a randomly selected baby of this type exceeds 4000 g? Is between 3000 and 4000 g? b. What is the probability that the birth weight of a randomly selected baby of this type is either less than 2000 g or greater than 5000 g? c. What is the probability that the birth weight of a randomly selected baby of this type exceeds 7 lb? d. How would you characterize the most extreme .1% of all birth weights? e. If X is a random variable with a normal distribution and a is a numerical constant (a ≠ O),then Y= ax also has a normal distribut Use this to determine the distribution of birth weight expressed in pounds(shape, mean, and standard deviaion), and then recalculate the probability frompart (c) . How does this compare to your previous question.

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Description: Consider babies born in the "normal" range of 37-43 weeks gestational age.Extensive data supports the assumption that for such babies born in the United States,birth weight is normally distributed with mean 3432 g and standard deviation 482 g.[The ar

MATLAB: An Introduction with Applications

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ISBN:9781119256830

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Consider babies born in the "normal" range of 37-43 weeks gestational age.Extensive data supports the assumption that for such babies born in the United States,birth weight is normally distributed with mean 3432 g and standard deviation 482 g.[The article "Are Babies Normal?" (The American Statistician, 1999:298-302) analyzed data from a particular year;for a sensible choice of class intervals,a histogram did not look at all normal,but after further investigations it was determined that this was due to some hospitals measuring weight in grams and others measuring to the nearest ounce and then converting to grams. A modified choice of class intervals that allowed for this gave a histogram that was well described by a normal distribution.)

a. What is the probability that the birth weight of a randomly selected baby of this type exceeds 4000 g? Is between 3000 and 4000 g?

b. What is the probability that the birth weight of a randomly selected baby of this type is either less than 2000 g or greater than 5000 g?

c. What is the probability that the birth weight of a randomly selected baby of this type exceeds 7 lb?

d. How would you characterize the most extreme .1% of all birth weights?

e. If X is a random variable with a normal distribution and a is a numerical constant (a ≠ O),then Y= ax also has a normal distribut Use this to determine the distribution of birth weight expressed in pounds(shape, mean, and standard deviaion), and then recalculate the probability frompart (c) . How does this compare to your previous question.

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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