The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 13 days. **Pregnancy Length Analysis in a Rural Village**The lengths of pregnancies in a small rural village follow a normal distribution, characterized by:- **Mean:** 267 days- **Standard Deviation:** 13 days**Questions for Analysis:**1. **Range for Middle 95% of Pregnancies:** - Determine the range where you would expect to find the middle 95% of pregnancy lengths. - Input your range estimates in the form of numbers accurate to one decimal place. - **Input Fields:** - Between [_____] and [_____].2. **Range for Middle 95% of Sample Averages:** - If samples of size 37 are drawn from the population, identify the range for the middle 95% of sample averages for pregnancy lengths. - Again, enter your estimates as numbers with one decimal place of accuracy. - **Input Fields:** - Between [_____] and [_____].Ensure your answers are precise and consider standard statistical methods to determine these ranges.

μ = 267σ = 13 C = 95% α = 1 - 0.95 = 0.05 α2 = 0.025 zα2 = ±1.96 The middle 95% of most…

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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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The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 13 days.

**Pregnancy Length Analysis in a Rural Village**

The lengths of pregnancies in a small rural village follow a normal distribution, characterized by:

- **Mean:** 267 days
- **Standard Deviation:** 13 days

**Questions for Analysis:**

1. **Range for Middle 95% of Pregnancies:**
- Determine the range where you would expect to find the middle 95% of pregnancy lengths.
- Input your range estimates in the form of numbers accurate to one decimal place.
- **Input Fields:**
- Between [_____] and [_____].

2. **Range for Middle 95% of Sample Averages:**
- If samples of size 37 are drawn from the population, identify the range for the middle 95% of sample averages for pregnancy lengths.
- Again, enter your estimates as numbers with one decimal place of accuracy.
- **Input Fields:**
- Between [_____] and [_____].

Ensure your answers are precise and consider standard statistical methods to determine these ranges.

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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