Concept explainers
a.
To calculate: The percent of loaves with weights that are less than 450 grams.
a.
Answer to Problem 5WE
The percent of loaves with weights that are less than 450 grams is
Explanation of Solution
Given information:
For a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
Formula used:
The number x is known as standardized value to z where z is provided value of
Calculation:
Consider the provided information that for a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
To compute percent of loaves with weights that are less than 450 grams.
Recall that the number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Here, z is 450, m is 455 and
Apply it,
The total area under the curve is 1 and standard normal curve is symmetric about y -axis.
The required percent is the area under the curve of standard normal to the left of
Multiply the result by 100, to obtain the answer in percentage form,
Thus, the percent of loaves with weights that are less than 450 grams is
b.
To calculate: The percent of loaves with weights that are greater than 445 grams.
b.
Answer to Problem 5WE
The percent of loaves with weights that are greater than 445 grams is
Explanation of Solution
Given information:
For a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
Formula used:
The number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Calculation:
Consider the provided information that for a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
To compute percent of loaves with weights that are greater than 445 grams.
Recall that the number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Here, z is 445, m is 455 and
Apply it,
The total area under the curve is 1 and standard normal curve is symmetric about y -axis.
The required percent is the area under the curve of standard normal to the right of
Multiply the result by 100, to obtain the answer in percentage form,
Thus, the percent of loaves with weights that are greater than 445 grams is
c.
To calculate: The percent of loaves with weights that are greater than 470 grams.
c.
Answer to Problem 5WE
The percent of loaves with weights that are greater than 470 grams is
Explanation of Solution
Given information:
For a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
Formula used:
The number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Calculation:
Consider the provided information that for a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
To compute percent of loaves with weights that are greater than 470 grams.
Recall that the number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Here, z is 470, m is 455 and
Apply it,
The total area under the curve is 1 and standard normal curve is symmetric about y -axis.
The required percent is the area under the curve of standard normal to the right of
Multiply the result by 100, to obtain the answer in percentage form,
Thus, the percent of loaves with weights that are greater than 470 grams is
d.
To calculate: The percent of loaves with weights that are between 450 grams and 460 grams.
d.
Answer to Problem 5WE
The percent of loaves with weights that are between 450 grams and 460 gramsis
Explanation of Solution
Given information:
For a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
Formula used:
The number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Calculation:
Consider the provided information that for a loaf of a bread the mean weight is 455 grams and standard deviation is 5 grams.
To compute percent of loaves with weights that are between 450 grams and 460 grams.
Recall that the number x is known as standardized value to z where z is provided value of normal distribution, m is the mean and
Here, z is 450, m is 455 and
Apply it,
Also, here, z is 460, m is 455 and
Apply it,
The total area under the curve is 1 and standard normal curve is symmetric about y -axis.
The required percent is the area under the curve of standard normal between
Multiply the result by 100, to obtain the answer in percentage form,
Thus, the percent of loaves with weights that is between 450 grams and 460 gramsis
Chapter 15 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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