1. Birth weights of babies in the United States can be modeled by a normal distribution with mean 3250 grams and standard deviation 550 grams. Those weighing less than 2500 grams are considered to be of low birth weight. (a) Sketch a normal distribution curve and shade in the region whose area corresppnds to the probability that a baby will have a low birth weight. (The prohalailety that binth weigh is less than 2500=.08634 3250 -SSO density 2700 2760 (b) Based on this shaded region (using the Empirical Rule and remembering that the total area under the normal curve is 1), make an educated guess for the proportion of babies born with a low birth weight. (c) Using Excel, find the proportion of babies born with a low birth weight. How did your computed answer compare to your educated guess?

1. Birth weights of babies in the United States can be modeled by a normal distribution with mean 3250 grams and standard deviation 550 grams. Those weighing less than 2500 grams are considered to be of low birth weight. (a) Sketch a normal distribution curve and shade in the region whose area corresppnds to the probability that a baby will have a low birth weight. (The prohalailety that binth weigh is less than 2500=.08634 3250 -SSO density 2700 2760 (b) Based on this shaded region (using the Empirical Rule and remembering that the total area under the normal curve is 1), make an educated guess for the proportion of babies born with a low birth weight. (c) Using Excel, find the proportion of babies born with a low birth weight. How did your computed answer compare to your educated guess?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

100%

(g) How little would a baby have to weigh to be among the lightest 2.5% of all newborns? [Start with a sketch]
(h) How much would a baby have to weigh to be among the heaviest 10% of all newborns? [Start with a sketch]
2. In the mid-19 century, Sir Francis Galton demonstrated, through extensive data collection, that many human
characteristics such as height and IQ are distributed throughout the entire population in accordance with the normal
distribution. Galton recorded the heights of 8585 men in Great Britain. This forms a normal distribution with a mean
of 67 inches and standard deviation of 2.5 inches.
(a) Graph this normal distribution and label the x-axis.
(b) What proportion of these men were between 66 and 68 inches tall?
(c) What fraction of the adult male population in Great Britain was within one standard deviation of the mean
height? [Use the normal distribution function in Excel, not the Empirical Rule]
(d) What height corresponds to the 95th percentile in the Galton study?

Normal Distribution Review
1. Birth weights of babies in the United States can be modeled by a normal distribution with mean 3250 grams and
standard deviation 550 grams. Those weighing less than 2500 grams are considered to be of low birth weight.
(a) Sketch a normal distribution curve and shade in the region whose area correspopnds to the probability that a
baby will have a low birth weight.
(The probulalety that binth
weeighis less than 2500=.08634
3250
density
-sSO
2700
2760 370 380 4350
(b) Based on this shaded region (using the Empirical Rule and remembering that the total area under the normal
curve is 1), make an educated guess for the proportion of babies born with a low birth weight.
(c) Using Excel, find the proportion of babies born with a low birth weight. How did your computed answer compare
to your educated guess?
(d) What proportion of babies would the normal distribution predict as weighing more than 10 pounds (4536 grams)
at birth? [Hint: Always start with a sketch of the normal curve and the area you are looking for. Then use Excel]
10,000
Dens
2251
4536
(e) Determine the probability that a randomly selected baby weighs between 3000 and 4000 grams at birth. [Start
with a sketch]
=.5889
Dersr
310)3250 4000
(f) Data from the National Vital Statistics Report indicate that there were 3,880,894 births in the United States in
1997. A total of 291,154 babies were of low birth weight, while 2,552,852 babies weighed between 3000 and 4000
grams. Compute the observed proportions in each of these two groups, and comment on how well the normal
calculations approximates these values.

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