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Answer:
54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Lesser than 207.9.
pvalue of Z when X = 207.9. So
By the Central Limit Theorem
has a pvalue of 0.2743
2*0.2743 = 0.5486
54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Answer: C. Y = 5x + 5
Step-by-step explanation:
We need to write, or decide on, the equation for the blue line as this line represents the trend line for this scatter plot. We will write this in slope-intercept form. <em>See attached for a visual</em>.
First, we will find our slope. We will use for this since we have a graph with clear points. See attached, we count up [5] and then count to the right [1] for a slope of 5.
-> Slope = 5
Now, we will find our y-intercept. This is where the line intersects the y-axis. The line hits the y-axis at point (0, 5) giving us a y-intercept of 5.
-> Y-intercept = 5
Lastly, we will write our equation and decide on an answer.
y = <em>m</em>x + <em>b</em>
y = (5)x + (5)
Y = 5x + 5
C. Y = 5x + 5
