Let the continuous random variable D denote the diameter of the hole drilled in an aluminum...

Let the continuous random variable D denote the diameter of the hole drilled in an
aluminum sheet. The target diameter to be achieved is 12.5mm. Random
disturbances in the process often result in inaccuracy.
Historical data shows that the distribution of D can be modelled by the PDF, f(d) =
20e−20(d−12.5), d ≥ 12.5. If a part with diameter > 12.6 mm needs to be scrapped,
what is the proportion of those parts? What is the CDF when the diameter is of 11
mm?
What is the conclusion of this experiment?

Problem Statement 10:

Please compute the following:
a) P(Z > 1.26), . P(Z < −0.86), P(Z > −1.37), P(−1.25 < Z < 0.37), . P(Z ≤ −4.6)
b) Find the value z such that P(Z > z) = 0.05
c) Find the value of z such that P(−z < Z < z) = 0.99

Expert Solution

orchestra answered 1 year ago

let the continuous random variable D denotes the diameter of the hole drilled in an aluminium...

let the continuous random variable D denotes the diameter of the hole drilled in an aluminium sheet. The target diameter to be achieved is 12.5mm. Random disturbances in the process often result in accuracy. historical data shows that the distribution of D can be modelled by the PDF (d)= 20e-20(d-12.5), d>=12.5. If a part with diameter >12.6mm needs to be scrapped, what is the proportion of those parts? what is the CDF when the diameter is of 11mm? what is...

Let z denote a random variable having a normal distribution with ? = 0 and ?...

Let z denote a random variable having a normal distribution with ? = 0 and ? = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.3) = (b) P(z < -0.3) = (c) P(0.40 < z < 0.85) = (d) P(-0.85 < z < -0.40) = (e) P(-0.40 < z < 0.85) = (f) P(z > -1.26) = (g) P(z < -1.5 or z > 2.50) =

A 3/4" diameter hole is to be drilled through 3/4" thick piece of steel plate. The...

A 3/4" diameter hole is to be drilled through 3/4" thick piece of steel plate. The twist drill is to be fed at 0.025 ipr. Maximum cutting speed of 70 fpm is recommended. Calculate: A) Cutting time B) Metal Removal Rate (MRR)

Let the random variable X denote the time (hours) for which a part is waiting for...

Let the random variable X denote the time (hours) for which a part is waiting for the beginning of the inspection process since its arrival at the inspection station, and let Y denote the time (hours) until the inspection process is completed since its arrival at the inspection station. Since both X and Y measure the time since the arrival of the part at the inspection station, always X < Y is true. The joint probability density function for X...

Let x be a continuous random variable that follows a distribution skewed to the left with...

Let x be a continuous random variable that follows a distribution skewed to the left with ?= 92 and ?=15. Assuming n/N <= .05, find the probability that the sample mean, x bar, for a random sample of 62 taken from this population will be (ROUND ANSWERS TO FOUR DECIMAL PLACES): a) less than 81.5 P(less that 81.5)= b) greater than 89.7 P(greater than 89.7)= Please show your work.

Let x be a continuous random variable that is normally distributed with a mean of 65...

Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value: less than 48 greater than 87 between 56 and 70

Let be a continuous random variable that has a normal distribution with μ = 48 and...

Let be a continuous random variable that has a normal distribution with μ = 48 and σ = 8. Assuming , n/N ≤ 0.05, find the probability that the sample mean, x , for a random sample of 16 taken from this population will be more than 45.30 . Round your answer to four decimal places.

Two dice are rolled. Let the random variable X denote the number that falls uppermost on...

Two dice are rolled. Let the random variable X denote the number that falls uppermost on the first die and let Y denote the number that falls uppermost on the second die. (a) Find the probability distributions of X and Y. x 1 2 3 4 5 6 P(X = x) y 1 2 3 4 5 6 P(Y = y) (b) Find the probability distribution of X + Y. x + y 2 3 4 5 6 7 P(X...

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 0.2) = (b) P(z < -0.2) = (c) P(0.40 < z < 0.86) = (d) P(-0.86 < z < -0.40) = (e) P(-0.40 < z < 0.86) = (f) P(z > -1.24) = (g) P(z < -1.5 or z > 2.50) =

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ = 1. Determine each of the following probabilities. (Round all answers to four decimal places.) (a) P(z < 0.1) = (b) P(z < −0.1) = (c) P(0.40 < z < 0.85) = (d) P(−0.85 < z < −0.40) = (e) P(−0.40 < z < 0.85) = (f) P(z > −1.25) = (g) P(z < −1.5 or z > 2.50) = Let z denote a...

Question

Let the continuous random variable D denote the diameter of the hole drilled in an aluminum...

Solutions

Expert Solution

Related Solutions

let the continuous random variable D denotes the diameter of the hole drilled in an aluminium...

Let z denote a random variable having a normal distribution with ? = 0 and ?...

A 3/4" diameter hole is to be drilled through 3/4" thick piece of steel plate. The...

Let the random variable X denote the time (hours) for which a part is waiting for...

Let x be a continuous random variable that follows a distribution skewed to the left with...

Let x be a continuous random variable that is normally distributed with a mean of 65...

Let be a continuous random variable that has a normal distribution with μ = 48 and...

Two dice are rolled. Let the random variable X denote the number that falls uppermost on...

Let z denote a random variable having a normal distribution with μ = 0 and σ...

Let z denote a random variable having a normal distribution with μ = 0 and σ...