10 The compressive strength of samples of cement can be mode

10. The compressive strength of samples of cement can be modeled by a normal distribution with a means of 6000 kg/cm^2 and a standard deviation of 100 kg /cm^2 . (a) What is the probability that a sample\'s-strength is less than 6250 kg/cm^2? (b) What is the probability that a sample\'s strength is between 5800 and 5900 kg/cm^2? (c) What strength is exceeded by 95% of the samples?

Solution

Mean = u = 6000
SD = 100

a) LEss than 6250

z = (x - u) / SD
z = (6250 - 6000) / 100
z = 2.5

P(z < 2.5) is to be found

Use this link ----> https://www.easycalculation.com/statistics/p-value-for-z-score.php

And plug in z = 2.5 and check the left tailed value.....

0.9938 ---> ANSWER

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z = (x - u) / SD
z = (5800 - 6000) / 100
z = -2

P(z < -2) = 0.0228

z = (x - u) / SD
z = (5900 - 6000) / 100
z = -1

P(z < -1) = 0.1587

P(-2 < z < -1) = 0.1587 - 0.0228 ----> 0.1359 --> ANSWER

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If 95% of the samples exceed, then 5% is lower...

So, check this link ----> http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf

When P = 0.05, z = -2.575 approx

z = (x - u) / SD

-2.575 = (x - 6000) / 100

-257.5 = x - 6000

x = 6000 - 257.5

x = 5742.5

So, a value of 5742.5 is exceeded by 95% of the sample.... ---> ANSWER