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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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Question

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean

μ=293 days

and standard deviation

σ=21 days.

Complete parts (a) through (f) below.

(a) What is the probability that a randomly selected pregnancy lasts less than

285

days?

The probability that a randomly selected pregnancy lasts less than

285

days is approximately

. 3516.3516.

(Round to four decimal places as needed.)

Interpret this probability. Select the correct choice below and fill in the answer box within your choice.

(Round to the nearest integer as needed.)

If 100 pregnant individuals were selected independently from this population, we would expect

nothing

pregnancies to last exactly

285

days.

If 100 pregnant individuals were selected independently from this population, we would expect

nothing

pregnancies to last more than

285

days.

If 100 pregnant individuals were selected independently from this population, we would expect

3535

pregnancies to last less than

285

days.

Your answer is not correct.

(b) Suppose a random sample of

pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

The sampling distribution of

▼

with

μx=nothing

and

σx=nothing.

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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