Chapter 7, section 7.2, question p9 the process for manufacturing a ball bearing results in weights that have an approximately normal distribution with mean 0.15 g and standard deviation 0.005 g. a. if you select one ball bearing at random, what is the probability that it weighs less than 0.149 g? (round to four decimal places) b. if you select four ball bearings at random, what is the probability that their mean weight is less than 0.149 g? (round to four decimal places) c. if you select ten ball bearings at random, what is the probability that their mean weight is less than 0.149 g? (round to four decimal places)

a. Let be a random variable representing the weight of a ball bearing selected at random. We're told that , so

where . This probability is approximately

b. Let be a random variable representing the weight of the -th ball that is selected, and let be the mean of these 4 weights,

The sum of normally distributed random variables is a random variable that also follows a normal distribution,

so that

Then

c. Same as (b).

this doesn't make sense lol

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.