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zzz [600]
3 years ago
7

The lengths of 3-inch nails manufactured on a machine are normally distributed with a mean of 3.0 inches and a standard deviatio

n of .009 inch. The nails that are either shorter than 2.98 inches or longer are than 3.02 inches are unusable. What percentage of all the nails produced by this machine are unusable?
Mathematics
1 answer:
otez555 [7]3 years ago
7 0

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 \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • 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 \mu = 3.
  • The standard deviation is of 0.009 inches, hence \sigma = 0.009.

Nails that are <u>more than 0.02 inches</u> from the mean are unusable, hence:

Z = \frac{0.02}{\sigma}

Z = \frac{0.02}{0.009}

Z = 2.22

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

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Answer:

Option C: 38 is p more than 25

Step-by-step explanation:

the equation 25 + p = 38

can be read as 38 is 25 plus p units, or similarly ;

38 is p units more than 25.

Therefore from the three sentences you are showing, only the last one (option C) is the correct one.

4 0
3 years ago
Megan uses cup of almonds to make 4 cups of trail mix. Using this
djverab [1.8K]
Answer:
2 1/4 cups

Step by step:
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2 years ago
If f(x) = x^2 - 2x and g(x) = 6x + 4, for which value of x does (f+g)(x) = 0?
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3 0
3 years ago
What is the 13th term of the geometric sequence<br> 4, 12, 36, 108, ...?
bogdanovich [222]

Answer: 2,125,764

Step-by-step explanation:

You can use the equation y=ar^n-1 to find the 13th term where a is the starting term, r is the common ratio, and n is the nth term

The next number is 12/4=3 times greater than the first. So if this sequence is a geometric one, then the next term must be 12*3=36. This is true, and the next term must be 36*3=108, which is also true. Therefore this sequence is a geometric one and its common ratio is 3. Therefore the equation is:

y=4*3^(n-1)

Substitute 13 for n:

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Therefore, the 13th term of this geometric sequence is 2,125,764

7 0
2 years ago
On Monday, a local hamburger shop sold a combined total of 556 hamburgers and cheeseburgers. The number of cheeseburgers sold wa
Klio2033 [76]
H = number of hamburgers sold.
c = number of cheeseburgers sold.

we know that "c" is three times the number of "h", thus c = 3h

we also know, the total amount sold for both is 556,  h + c = 556

h + c = 556
c = 3h
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what about "c"? well, c = 3h
7 0
3 years ago
Read 2 more answers
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