Mathematics, 14.04.2020 18:39 bskyeb14579

A process manufactures ball bearings with diameters that are normally distributed with mean 25.1 mm and standard deviation 0.08 mm. What proportion of the diameters are less than 25.0 mm? Find the 10th percentile of the diameters. A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on? To meet a certain specification, a ball bearing must have a diameter between 25.0 and 25.3 millimeters. What proportion of the ball bearings meet the specification?

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Answer from: random286

a) 10.57% of the diameters are less than 25.0 mm

b) The 10th percentile of the diameters is 25.2024 mm

c) A diameter of 25.2 mm is on 89.44th percentile.

d) 88.81% of the diameter is between 25.0 and 25.3 millimeters

Step-by-step explanation:

Given that:

mean μ = 25.1 mm

standard deviation σ = 0.08 mm

a) What proportion of the diameters are less than 25.0 mm?

The Z score is given by the equation:

$z=\frac{x-\mu}{\sigma}$

For diameter of 25mm

$z=\frac{x-\mu}{\sigma}=\frac{25-25.1}{0.08} =-1.25$

P(X < 25) = P(z < -1.25) = 0.1057 = 10.57%

10.57% of the diameters are less than 25.0 mm

b) Find the 10th percentile of the diameters

10th percentile = 0.1. From z table, the the 10th percentile corresponds with a z score of -1.28

$z=\frac{x-\mu}{\sigma}\\-1.28=\frac{x-25.1}{0.08}\\ x-25.1=-1.024\\x=25.2024$

The 10th percentile of the diameters is 25.2024 mm

c) A particular ball bearing has a diameter of 25.2 mm. What percentile is its diameter on

The Z score is given by the equation:

$z=\frac{x-\mu}{\sigma}$

For diameter of 25.2 mm

$z=\frac{x-\mu}{\sigma}=\frac{25.2-25.1}{0.08} =1.25$

P(X < 25.2) = P(z < 1.25) = 0.8944 = 89.44%

A diameter of 25.2 mm is on 89.44th percentile.

d) To meet a certain specification, a ball bearing must have a diameter between 25.0 and 25.3 millimeters. What proportion of the ball bearings meet the specification

For diameter of 25 mm

$z=\frac{x-\mu}{\sigma}=\frac{25-25.1}{0.08} =-1.25$

For diameter of 25.3 mm

$z=\frac{x-\mu}{\sigma}=\frac{25.3-25.1}{0.08} =2.5$

P(25 < X < 25.3) = P(-1.25 < z < 2.5) = P(z < 2.5) - P(z < -1.25) = 0.9938 - 0.1057 = 0.8881 = 88.81%

88.81% of the diameter is between 25.0 and 25.3 millimeters

Answer from: Quest

A. p = 2(l + w)p/2 - l = ww = p/2 - l b. while isolating the variable w in the equation, i first divided both sides by 2 and then i subtracted l from both sides. i hope this .

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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