Chapter 7: Q. 38 (page 429)

A manufacturer produces $25$ -pound lifting weights. The lowest actual weight is $24$ pounds, and the highest is $26$ pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of $100$ weights is taken.
Draw the graph from Exercise $7.37$

Short Answer

Expert verified

The probability that the mean actual weight for the $100$ weights is less than $24.9$ is given by the following graph

Step by step solution

Given Information

We have $25$ -pound lifting weights. The lowest actual weight is $24$ pounds, and the highest is $26$ pounds. The distribution of weights is uniform

Explanation

From example, $7.37$ we know

The mean of uniform distribution is

$μ_{X} = \frac{a + b}{2}$

$= \frac{24 + 26}{2}$

$= 25$

The standard deviation is

$σ_{x} = \sqrt{\frac{(b - a)^{2}}{12}}$

$= \sqrt{\frac{(26 - 24)^{2}}{12}}$

$= \sqrt{\frac{4}{12}}$

$= 0.5774$

The distribution of the mean weight of $100, 25$ -pounds is

$\bar{X} ~ N (μ_{X}, σ_{X} / \sqrt{n})$

$\bar{X} ~ N (25, 0.0577)$

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A manufacturer produces $25$ -pound lifting weights. The lowest actual weight is $24$ pounds, and the highest is $26$ pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of $100$ weights is taken.
Draw the graph from Exercise $7.37$

Short Answer

Step by step solution

Given Information

Explanation

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A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24pounds, and the highest is 26pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of100weights is taken.Draw the graph from Exercise7.37

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Calculus

Pure Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

A manufacturer produces $25$ -pound lifting weights. The lowest actual weight is $24$ pounds, and the highest is $26$ pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of $100$ weights is taken.
Draw the graph from Exercise $7.37$