Answered: Assume that the duration of human pregnancies can be described by a Normal model with mean 265 days and standard deviation 13 days. a) What percentage of…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

Assume that the duration of human pregnancies can be described by a Normal model with mean

265

days and standard deviation

days.

a) What percentage of pregnancies should last between

269

and

276

days?

b) At least how many days should the longest

30%

of all pregnancies last?

c) Suppose a certain obstetrician is currently providing prenatal care to

pregnant women. Let

represent the mean length of their pregnancies. According to the Central Limit Theorem, what's the distribution of this sample mean,

Specify themodel, mean, and standard deviation.

d) What's the probability that the mean duration of these patients' pregnancies will be less than

262

days?

a) The percentage of pregnancies that should last between

269

and

276

days is

nothing%.

(Round to two decimal places as needed.)

b) The longest

30%

of all pregnancies should last at least

nothing

days.

(Round to one decimal place as needed.)

c) Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.

A Normal model with mean

nothing

and standard deviation nothing

(Type integers or decimals rounded to two decimal places as needed.)

A Binomial model with

nothing

trials and a probability of success of nothing

(Type integers or decimals rounded to two decimal places as needed.)

There is no model that fits this distribution.

d) The probability that the mean duration of these patients' pregnancies will be less than

262

days is

nothing.

(Round to four decimal places as needed.)

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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