Answer:
(a)
Step-by-step explanation:
Given
See attachment for sets A and B
Required
The true statement about both sets
First, we calculate the typical values (mean) of set A and set B.
This is calculated as:

For A:



For B:



<em>Here, we can conclude that B has a larger typical value</em>
Next calculate the spread (range) of sets A and B
This is calculated as:

For A:


For B


<em>Here, we can conclude that A has a larger spread.</em>
<em></em>
<em>Hence, (a) is true</em>
Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.
In a <em>normal distribution</em> with mean
and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
- The mean is of 3 inches, hence
.
- The standard deviation is of 0.009 inches, hence
.
Nails that are <u>more than 0.02 inches</u> from the mean are unusable, hence:



The proportion is P(|Z| > 2.22), which is <u>2 multiplied by the p-value of Z = -2.22</u>.
Z = -2.22 has a p-value of 0.0132.
2 x 0.0132 = 0.0264
0.0264 x 100% = 2.64%
2.64% of all the nails produced by this machine are unusable.
You can learn more about the normal distribution at brainly.com/question/24663213
Answer:
what?
Step-by-step explanation: