A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of
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Answer:
Step-by-step explanation:
This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.
Where <em>a</em> and <em>b </em> are the legs of the triangle and <em>c</em> is the hypotenuse.
In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:
Substitute these values into the formula.
Solve the exponents.
- (7)²= 7*7=49
- (√15)²=√15*√15=15
Add.
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
The third side length is <u>8.</u>
Answer:
0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.
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 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.
Mean of 17.42 ppm and a standard deviation of 3.25 ppm.
This means that
Sample of 12:
This means that
Find the probability that the mean printing speed of the sample is greater than 18.12 ppm.
This is 1 subtracted by the p-value of Z when X = 18.12.
By the Central Limit Theorem
has a pvalue of 0.773.
1 - 0.773 = 0.227
0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.