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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:
C.I = 0.108 ± 0.022
Step-by-step explanation:
In this case, we are given a symmetric confidence interval, and the sample proportion p', is derived by finding the average of the two values.
Therefore, the sample proportion will be:
= 0.108
p' = 0.108
To find the margin of error, we have:
M.E = ½ * length of confidence interval
Where length of confidence interval = 0.130 - 0.086
= 0.044
Therefore,
Margin of error = 0.022
The confidence interval is expressed as:
p' ± M.E
= 0.108 ± 0.022