In the table below, y is directly proportional to x. Determine the constant of proportionality. Explain how you found your answe
1 answer:
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Answer:
The probability that the diameter falls in the interval from 2499 psi to 2510 psi is 0.00798.
Step-by-step explanation:
Let's define the random variable, "Comprehensive strength of concrete". We have information that
is normally distributed with a mean of 2500 psi and a standard deviation of 50 psi (or a variance of 2500 psi). In other words,
.
We want to know the probability of the mean of X or that falls in the interval
. From inference theory we know that :
Now we can find the probability as follows:
Where , then:
Answer:
Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.
Step-by-step explanation:
Problems of normally distributed samples can be 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.
In this problem, we have that:
Top 5%:
X when Z has a pvalue of 0.95. So X when Z = 1.645
Bottom 5%:
X when Z has a pvalue of 0.05. So X when Z = -1.645
Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.