Suppose there are three routes from North Point to Boulder Creek, four routes from Boulder Creek to Beaver Dam, four routes from
1 answer:
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Answer:
0.73% probability that their mean length is less than 11.1 inches
Step-by-step explanation:
To solve this question, we have 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation, which is also called standard error
In this problem, we have that:
What is the probability that their mean length is less than 11.1 inches
This is the pvalue of Z when X = 11.1. So
By the Central Limit Theorem
has a pvalue of 0.0073.
0.73% probability that their mean length is less than 11.1 inches
The first step that we must take before attempting to solve the problem is to understand what the problem statement is asking us to do and what is given to us to help accomplish that goal. Looking at the problem statement we can see that we are being asked to write an equation. The information that is provided to us is the slope of the line and a point through which the line crosses.
Now that we have determine the important aspects of the problem, we can move onto the actual calculations of the problem which can start off by us plugging information into the point-slope form. But before plugging in the values we should understand what makes up the form.
⇒ This variable captures the y-coordinate of the coordinate that is provided in the problem through which the line crosses.
⇒ This variable capture the slope of the line that we will need to determine.
⇒ This variable captures the x-coordinate of the coordinate that is provided in the problem through which the line crosses.
<u>Plug in values</u>
Now that we have plugged in all of the values into the variables that need to be altered we can begin distributing on the right side and then solving for y.
<u>Distribute</u>
We are almost done with solving for y and the only step that we have left is to add 1.5 to both sides. This will remove it from the left side and isolate y which will give us the equation of the line that we need.
<u>Add 1.5 to both sides</u>
Now that we have fully simplified the expression using the slope and point that was given to us, we were able to determine that the equation that represents that line is y = -2.5x + 6.5