×
Log in to StudySoup
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 4 - Problem 49e
Join StudySoup for FREE
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 4 - Problem 49e

Already have an account? Login here
×
Reset your password

# Consider babies born in the “normal” range of 37–43 weeks

ISBN: 9780321629111 32

## Solution for problem 49E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Probability and Statistics for Engineers and the Scientists | 9th Edition

4 5 1 414 Reviews
24
2
Problem 49E

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.? ow 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 ?0), then Y = aX also has a normal distribution. Use this to determine the distribution of birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from part (c). How does this compare to your previous answer?

Step-by-Step Solution:

Answer : Step 1 of 5 : Given, 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. a) The claim is to find the probability that the birth weight of a randomly selected baby of this type exceeds 4000 g and Is between 3000 and 4000 g P(x > 4000) = 1 - P(x 4000) = 1 - (z x ) Where, x = 4000, = 3432 and = 482 Therefore, P(x > 4000) = 1 - (z 4000 3432) 482 = 1 - (z 1.178) = 1 - 0.8810 ( from the area under normal curve) = 0.119 Therefore, P(x > 4000) = 0.119 Then, between 3000 and 4000 P(3000 < x < 4000) = P(x 4000) - P(x3000) 4000 3432 3000 3432 = (z 482 ) - (z 482 ) = (z 1.178) - (z -0.896) = 0.8810 - 0.1867 = 0.6943 Therefore, P(3000 < x < 4000) = 0.6943

Step 2 of 5

Step 3 of 5

##### ISBN: 9780321629111

This full solution covers the following key subjects: weight, birth, normal, distribution, Probability. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “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.? ow 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 ?0), then Y = aX also has a normal distribution. Use this to determine the distribution of birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from part (c). How does this compare to your previous answer?” is broken down into a number of easy to follow steps, and 270 words. Since the solution to 49E from 4 chapter was answered, more than 1795 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 49E from chapter: 4 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111.

#### Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Consider babies born in the “normal” range of 37–43 weeks