Can someone please tell me which of these graphs represent a function?
2 answers:
You might be interested in
Answer: Third option.
Step-by-step explanation:
Let be "x" the approximate actual width of the car (in feet).
According to the information provided in the exercise, you know that the scale of the model car is:
By definition, this can be written as a fraction:
Therefore, if you know that the width of the model car is 2.3 inches, you can set up the following proportion:
Finally, you must solve for "x" in order to find its value.
This is:
Answer:
64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 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 less than .2 inches?
This is the pvalue of Z when X = 200 + 0.2 = 200.2 subtracted by the pvalue of Z when X = 200 - 0.2 = 199.8. So
X = 200.2
By the Central Limit Theorem
has a pvalue of 0.8238
X = 199.8
has a pvalue of 0.1762
0.8238 - 0.1762 = 0.6476
64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches