Respuesta :
Answer:
A) 0.3336; B) 0.8531
Step-by-step explanation:
For part A,
We use the z-score formula for an individual score:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
Our X value is 332, our mean, μ, is 335, and our standard deviation, σ, is 7:
z = (332-335)/7 = -3/7 ≈ -0.43
Using a z table, we see that the area under the curve less than this (the probability that X is less than this value) is 0.3336.
For part B,
We use the z-score formula for the mean of a sample:
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our X-bar value is 332, our mean, μ, is 335, our standard deviation, σ, is 7, and our sample size, n, is 6:
z = (332-335)/(7÷√6) = 3/2.8577 ≈ 1.05
Using a z table, we see that the are under the curve to the left of this, or the probability less than this, is 0.8531.
The respective probability that a randomly selected bottle will have less than 332 ml of beer are; 0.3336 and 0.1469
What is the p-value of the statistic?
We are given;
Population mean; μ = 335
standard deviation; σ = 7
A) P(X < 332)
z = (332 - 335)/7
z = -0.43
From online p-value from z-score calculator, we have;
p-value = 0.3336
B) We want to find the probability that a randomly selected 6-pack of beer will have a mean amount less than 332 ml. Thus;
z = (x' - μ)/(σ/√n)
z = (332 - 335)/(7/√6)
z = 1.05
From online p-value from z-score calculator, we have;
p-value = 0.1469
Read more about p-value at; https://brainly.com/question/4621112
