How to solve -7-3x+2=-8x-8
2 answers:
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Answer:
The required equation is 3y=36 and the tape diagram is shown below.
Step-by-step explanation:
Consider the provided information.
We need to write a multiplication equation that has a solution of 12.
3y=36
We know we have to split 36 into three equal groups, so we have to divide by 3 to show this algebraically.
3y÷3=36÷3
y=12
Now check this with the help of tape diagram as shown.
Consider the figure 1.
This represents if 36 had to be split into three groups, how big would each group be?
By the tape diagram we concluded that the value of y is 12.
Answer:
There is a 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation
In this problem, we have that:
The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 33,208 miles, with a standard deviation of 2503 miles.
This means that .
What is the probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct?
This is the pvalue of Z when subtracted by the pvalue of Z when
By the Central Limit Theorem, we have t find the standard deviation of the sample, that is:
So
X = 33841
has a pvalue of 0.9616
X = 32575
has a pvalue of 0.0384.
This means that there is a 0.9616 - 0.0384 = 0.9232 = 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.