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An equation is formed of two equal expressions. There is no solution set of the equation 3x+13 = 3(x+6)+1.
<h3>What is an equation?</h3>An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation can be solved in the following manner,
Since both the sides of the equation are the same in terms of variable and the constant terms are not the same. Therefore, there is no solution set of the equation 3x+13 = 3(x+6)+1.
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Answer:
a) 0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51
b) 0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51
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:
(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 17 pins is at least 51?
Here
This probability is 1 subtracted by the pvalue of Z when X = 51. So
By the Central Limit Theorem
has a pvalue of 0.9890
1 - 0.989 = 0.011
0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51
(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?
Here
has a pvalue of 0.9999
1 - 0.9999 = 0.0001
0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51
Answer: x = 20.
Step-by-step explanation:
x and (3x + 10) combine to form a right angle, shown in the diagram by the small square joining the perpendicular lines.
Right angles are 90 degrees, so you can add both angles to get 90: