Consider babies born in the "normal" range of 37–43 weeks gestational age. A paper suggests that a normal distribution with mean ? = 3500 grams and standard deviation ? = 522 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected full-term baby. (a) What is the probability that the birth weight of a randomly selected full-term baby exceeds 4000 g? (Round your answer to four decimal places.) (b) What is the probability that the birth weight of a randomly selected full-term baby is between 3000 and 4000 g? (Round your answer to four decimal places.) (c) What is the probability that the birth weight of a randomly selected full-term baby is either less than 2000 g or greater than 5000 g? (Round your answer to four decimal places.) (d) What is the probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds? (Hint: 1 lb = 453.59 g. Round your answer to four decimal places.) (e) How would you characterize the most extreme 0.1% of all full-term baby birth weights? (Round your answers to the nearest whole number.) The most extreme 0.1% of birth weights consist of those greater than grams and those less than grams. (f) 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 formula to determine the distribution of full-term baby birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from part (d). (Round your answer to four decimal places.)

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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Consider babies born in the "normal" range of 37–43 weeks gestational age. A paper suggests that a normal distribution with mean

? = 3500 grams

and standard deviation

? = 522 grams

is a reasonable model for the probability distribution of the continuous numerical variable

x = birth weight

of a randomly selected full-term baby.

(a)

What is the probability that the birth weight of a randomly selected full-term baby exceeds 4000 g? (Round your answer to four decimal places.)

(b)

What is the probability that the birth weight of a randomly selected full-term baby is between 3000 and 4000 g? (Round your answer to four decimal places.)

(c)

What is the probability that the birth weight of a randomly selected full-term baby is either less than 2000 g or greater than 5000 g? (Round your answer to four decimal places.)

(d)

What is the probability that the birth weight of a randomly selected full-term baby exceeds 7 pounds? (Hint: 1 lb = 453.59 g. Round your answer to four decimal places.)

(e)

How would you characterize the most extreme 0.1% of all full-term baby birth weights? (Round your answers to the nearest whole number.)

The most extreme 0.1% of birth weights consist of those greater than grams and those less than grams.

(f)

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 formula to determine the distribution of full-term baby birth weight expressed in pounds (shape, mean, and standard deviation), and then recalculate the probability from part (d). (Round your answer to four decimal places.)

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