Answer: Third option
Step-by-step explanation:
You have the function:
Then, if the value of x increases by 1, you obtain:
-Rewrite the function:
-Substitute values for x into the function and observe what happen to y. Then:
x=1
x=2
x=3
The value of y is doubled.
Answer:
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Proportion of 0.6
This means that
Sample of 46
This means that
Mean and standard deviation:
Probability of obtaining a sample proportion less than 0.5.
p-value of Z when X = 0.5. So
By the Central Limit Theorem
has a p-value of 0.0838
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
The statement (A), statement (B), statement (D) are correct because the equation is y = 437.9x + 439.4
<h3>What is the line of best fit?</h3>A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
From the data given, we can calculate the correlation coefficient, slope of the line, and y-intercept.
r = 0.90
Since r is close to 1 shows a strong correlation.
Slope of the line of best fit = 437.9
Y-intercept of line of the best fit = 439.4(Refer to the attached picture)
The line will be:
y = 437.9x + 439.4
Thus, the statement (A), statement (B), statement (D) are correct because the equation is y = 437.9x + 439.4
Learn more about the line of best fit here:
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