Respuesta :
Answer: 0.0164
Step-by-step explanation:
Given : The standards for glass thickness call for the glass to average [tex]\mu=\text{ 0.375 inches}[/tex] with a standard deviation 0[tex]\sigma=\text{ 0.050 inch}[/tex].
[tex]H_0:\mu=0.375\\\\H_a:\mu\neq0.375[/tex]
Since the alternative hypothesis is two-tailed , so the test is two-tailed test.
Sample size : [tex]n=50[/tex] , a large sample ( n>30) so we use z-test.
Sample mean :-[tex]\overline{x}=0.392[/tex]
We assume its a normal distribution.
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{0.392-0.375}{\dfrac{0.050}{\sqrt{50}}}\approx2.40[/tex]
By using standard normal distribution table , the p-value =
[tex]0.0163951\approx0.0164[/tex]
Thus, the probability if the windows meet the standards = 0.0164
The probability if the windows meet the standards is 0.016.
Given
The standards for glass thickness call for the glass to average 0.375 inches with a standard deviation equal to 0.050 inches.
Suppose a random sample of nequals50 windows yields a sample mean of 0.392 inches.
Probability;
In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.
The value of probability if the windows meet the standards is given by;
[tex]\rm Z = \dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n} }}\\\\[/tex]
Substitute all the values in the formula;
[tex]\rm Z = \dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n} }}\\\\ \rm Z = \dfrac{0.392-0.375}{\dfrac{0.050}{\sqrt{50} }}\\\\ Z = \dfrac{0.392-0.375}{0.050} \times {\sqrt{50} }\\\\Z= \dfrac{0.017}{0.050} \times 7.07\\\\Z=0.34 \times 7.07\\\\Z=2.40[/tex]
By using a standard normal distribution table, the p-value is 0.016.
Hence, the probability if the windows meet the standards is 0.016.
To know more about probability click the link given below.
https://brainly.com/question/15351734
