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zzz [600]
2 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]2 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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Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketbal
sweet-ann [11.9K]

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

Mean (\mu)= 70 inches

Standard deviation (\sigma)= 3 inches

Average basket ball player (\bar{X}) = 79 inches

Since it is normally distributed assume with 5% significance .

So, it becomes,

Z>\frac{\bar{X}-\mu}{\sigma}\\\\Z>\frac{79-70}{3}\\\\Z>\frac{9}{3}\\\\Z>3\\\\\therefore\ P(Z>3)=1-0.9987=0.0013

At 0.05 level of significance , 0.0013 = 0.13% of the adult male population is taller than the average basketball player .

Hence, First Option is correct.

5 0
3 years ago
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Solve for x. -6 = x – 35
shepuryov [24]

Answer:

The answer is x=29

Step-by-step explanation:

-6 = x – 35

=-6+35=x-35+35

x=29

8 0
3 years ago
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2) Write an equation that passes through the<br> point (-2,5) and is parallel to y ==x+1.
Marta_Voda [28]

Answer:

y = x + 7

Step-by-step explanation:

5 = -2 + b

7 = b

y = x + 7

* Parallel lines have SIMILAR <em>RATE</em><em> </em><em>OF</em><em> </em><em>CHANGES</em><em> </em>[<em>SLOPES</em>], so 1 remains the way it is.

I am joyous to assist you anytime.

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Shoni's initial balance in her checking account is 674.48
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Joshua uses the escalator in the shopping mall to get to the ground floor from the underground garage located at (12,-5). Which
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Answer:

(4,5)

Step-by-step explanation:

Initial location of Joshua in the shopping mall is expressed according to the coordinate (12, -5)

If he undergoes a translation of 8 steps to the left and 10 steps upwards, this means that he moves 8 steps towards the negative x axis and 10 steps towards the positive y axis. The new coordinate will be gotten by adding the translation (-8, 10) to the initial coordinate as shown

New position = (12, -5) + (-8,10)

New position = (12-8, -5+10)

New position = (4, 5)

Hence the coordinates that corresponds to the location of the ground floor when undergoing a translation of 8 steps to the left and 10 steps upwards will be (4,5)

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