There you go:), hope was helpful
"The sum of the number 'n' and 31" . . . . . (n + 31)
"17 times the sum" . . . . . 17(n + 31)
The equation . . . . . 17(n + 31) = 357
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
Since 25% is smack in the middle between 20% and 30%, it will take equal volumes of ech to make a 25% solution.
Since 4 gallons of 30% solution was used, so 4 gallons of 20% solution will be needed.
Answer:
Confidence interval: (1760,1956)
Step-by-step explanation:
We are given the following information in the question:
Sample size, n = 81
Sample mean =

Population standard deviation =

Confidence Level = 95%
Significance level = 5% = 0.05
Confidence interval:

Putting the values, we get,

