Respuesta :
The probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3 is 0.16%.
The normal distribution is a type of probability function that describes how a variable's values are distributed. Since the majority of the observations cluster around the curve's middle peak, it is symmetric. In both directions, the probability for values of the distribution that are far from the mean.
Given that the fracture strength of tempered glass averages 14.1 (measured in thousands of pounds per square inch) and has standard deviation 2.
We have to determine what is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3?
We that μ = 14.1 σ = 2 n = 100 δ = 2/√100 = 0.2
This probability is 1 subtracted by the p-value of Z when X = 14.3. So
Z = (x-μ)/σ
By the Central Limit Theorem
Z = (x-μ)/δ
Z = (14.3 – 14.1)/0.2
Z = 0.2/0.2
Z = 1
Z =1 has a p-value is 0.8413
= 1 - 0.8413 = 0.1587
Therefore 0.16% is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.3.
To learn more about Normal Distribution Visit
https://brainly.com/question/25447725
#SPJ4
