Opposite number is the same number with the opposite sign:
So the opposite of
is 
, since the original number is positive
opposite of
is 
, since the original number is negative
So the opposite of
opposite of
Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If th
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Using the z-table, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 100
μ = mean = 125
σ = standard deviation = 18
z-score = (100 – 125) / 18
z-score = (-25) / 18
z-score = -1.39
Find the probability that corresponds to the z-score in the z-table. (see attached images)
-1.39 - (-1.3) : -1.4 - (-1.3) = x - 0.0968 : 0.0808 - 0.0968
-0.09 : -0.1 = x - 0.0968 : -0.016
x - 0.0968 = -0.09(-0.016)/-0.1
x = -0.0144 + 0.0968
x = 0.0824
x = 0.0824
Hence, the probability that a student taking this test will finish in 100 minutes or less is 0.0824 or 8.24%.
Learn more about probability here: brainly.com/question/26822684
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The confidence interval is 
.
We first find the mean. Add together all of the data points and divide by 6, the number of data points; the mean is 77.28.
Next we find the standard deviation. Find the difference between each data point and the mean; square it; find the sum; divide by the number of data points; take the square root. The standard deviation is 3.32.
To find the margin of error, we calculate the z-score associated with this level of confidence. 100-90 = 10% = 0.1; 0.1/2 = 0.05; 1-0.05 = 0.95. Using a z-table (http://www.z-table.com) we see that this is between two scores, 1.64 and 1.65; we will use 1.645.
The margin of error is given by
z * (σ/√n) = 1.645*(3.32/√6) = 2.23.
Thus the confidence interval is 77.28 +/ 2.23.
We first find the mean. Add together all of the data points and divide by 6, the number of data points; the mean is 77.28.
Next we find the standard deviation. Find the difference between each data point and the mean; square it; find the sum; divide by the number of data points; take the square root. The standard deviation is 3.32.
To find the margin of error, we calculate the z-score associated with this level of confidence. 100-90 = 10% = 0.1; 0.1/2 = 0.05; 1-0.05 = 0.95. Using a z-table (http://www.z-table.com) we see that this is between two scores, 1.64 and 1.65; we will use 1.645.
The margin of error is given by
z * (σ/√n) = 1.645*(3.32/√6) = 2.23.
Thus the confidence interval is 77.28 +/ 2.23.