Answered: Draw the density curve for the normal…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days.

a. Draw the density curve for the normal distribution of pregnancy lengths. Mark and label the location the mean and three standard deviations above and below the mean.

b. Answer the following questions using the density curve you drew for part a. It may help to shade relevant parts of the curve.

i. What percent of the pregnancies last between 250 and 282 days?

ii. What are the upper and lower bounds for the middle 95% of all pregnancy lengths?

iii. What percent of the pregnancies last between 218 and 314 days?

iv. What percent of the pregnancies last 266 days or fewer?

v. What percent of the pregnancies last between 266 and 282 days?

vi. What percent of the pregnancies last fewer than 250 days?

vii. What percent of the pregnancies last between 234 and 314 days?

viii. How long are the longest 2.5% of pregnancies?

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 + ...

Expert Solution