The production of a certain polymer fiber follows a normal distribution with a true mean diameter of 30 μm and a standard deviation of 20 μm. (a) Compute the probability of a measured value greater than 80 μm. (b) Compute the probability of a measured value between 60 and 75 μm.

Step-by-step explanation:

Since the the production of the polymer fiber follows a normal distribution, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = measured diameter values.

µ = mean diameter

σ = standard deviation

From the information given,

µ = 30 μm

σ = 20 μm

a) The probability of a measured value greater than 80 μm is expressed as

P(x > 80) = 1 - P(x ≤ 80)

For x = 80,

z = (80 - 30)/20 = 2.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.994

P(x > 80) = 1 - 0.994 = 0.006

b) the probability of a measured value between 60 and 75 μm is expressed as

P(60 ≤ x ≤ 75)

For x = 60,

z = (60 - 30)/20 = 1.5

The probability corresponding to the z score is 0.933

For x = 75,

z = (75 - 30)/20 = 2.25

The probability corresponding to the z score is 0.988

Therefore,

P(60 ≤ x ≤ 75) = 0.988 - 0.933 = 0.055

the multiples of 15 are 15, 30,45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195,   210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375,   390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, and 735.

the factors of 15 are 1, 3, 5, and 15.

hope that , fam!

-une, your fren : )

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)