Make a conjecture about the sum of the first 54 positive even numbers
1 answer:
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Answer:
0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component
Step-by-step explanation:
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.
Sum of normal variables:
When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.
The mean values are 20, 15, and 30 min, respectively:
This means that
The standard deviations are 1, 2, and 1.5 min, respectively.
This means that
What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?
Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.
has a pvalue of 0.0314
0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component
The value of the expression is
Explanation:
The expression is
The value of the expression can be determined using the rule PEMDAS.
According to the PEMDAS rule, first we need to perform the operation which is within the parenthesis.
Thus, the expression becomes,
Multiplying the values within parenthesis, we have,
Using PEMDAS, we need to multiply the numbers.
Again using PEMDAS rule, divide the number,
Finally, using PEMDAS, let us add the values, we have,
Thus, the value of the expression is