Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.
The most significant probability distribution in statistics for independent, random variables is the normal distribution, sometimes referred to as the Gaussian distribution. In statistical reports, its well-known bell-shaped curve is generally recognized.
The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare. Not all symmetrical distributions are normal, even though the normal distribution is symmetrical. The Student's t, Cauchy, and logistic distributions, for instance, are all symmetric.
The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics. Normal distributions are widely used to describe characteristics that are the sum of numerous distinct processes. For instance, the normal distribution is observed for heights, blood pressure, measurement error, and IQ scores.
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Answer:
The degrees of freedom are given by:
Now we can calculate the p value with the following probability:
And for this case since the p value is lower compared to the significance level 
we can reject the null hypothesis and we can conclude that the true mean for this case is different from 30.6 at the significance level of 0.05
Step-by-step explanation:
For this case we have the following info given:
represent the sample mean
represent the sample deviation
represent the reference value to test.
represent the sample size selected
The statistic for this case is given by:
And replacing we got:
The degrees of freedom are given by:
Now we can calculate the p value with the following probability:
And for this case since the p value is lower compared to the significance level we can reject the null hypothesis and we can conclude that the true mean for this case is different from 30.6 at the significance level of 0.05
You know how decimals are really long to write, like 0.00000000089? Well, with scientific notation, you can shorten them. Take the decimal I wrote for instance. Using scientific notation, I can change it to 8.9 * 10^-10. The decimal is shortened, and according to the exponent, 10^-10, we move the decimal place for 8.9 to the left ten places, leaving us with 0.00000000089.
Answer:
The system of equation used to find the dimension of the wooden deck in feet are 
.
Step-by-step explanation:
Given:
Perimeter of deck = 90 feet.
We need to find the system of equation used to determine the dimension in feet of the wooden deck.
Solution:
Let the length of the deck be 'l'.
Let the width of the deck be 'w'.
Now Given:
The deck's length, l, is 5 feet less than 4 times its width, w.
So we can say that;
Length of the deck is equal to 4 times width minus 5.
framing in equation form we get;
⇒ Equation 1
Now we know that;
Perimeter of the rectangle is given by 2 times Length times width of the rectangular deck.
framing in equation form we get;
⇒ Equation 2
Hence The system of equation used to find the dimension of the wooden deck in feet are .
