Mugs are packed into padded crates for shipping. Each crate contains 15 mugs. The mugs are normally distributed with a mean of 450g and a standard deviation of 5g. The weights of the empty crates are also normally distribute with a mean of 150g and a standard deviation of 13g. (a) Calculate the mean and variance for a fullncrate. (b) 90% of the full crates lie below a certain weight, what is that weight? use only maths and DO NOT USE THE EXCEL METHOD

Mugs are packed into padded crates for shipping. Each crate contains 15 mugs. The mugs are normally distributed with a mean of 450g and a standard deviation of 5g. The weights of the empty crates are also normally distribute with a mean of 150g and a standard deviation of 13g. (a) Calculate the mean and variance for a fullncrate. (b) 90% of the full crates lie below a certain weight, what is that weight? use only maths and DO NOT USE THE EXCEL METHOD

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Question

Mugs are packed into padded crates for shipping. Each crate contains 15 mugs. The mugs are normally distributed with a mean of 450g and a standard deviation of 5g. The weights of the empty crates are also normally distribute with a mean of 150g and a standard deviation of 13g.
(a) Calculate the mean and variance for a fullncrate.
(b) 90% of the full crates lie below a certain
weight, what is that weight?

use only maths and DO NOT USE THE EXCEL METHOD

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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