If an endpoint is included—shown by a closed dot, such as in the graph to the right—use = instead of ≤ or ≥ to indicate the numb
er is included. Complete the inequality for the domain. −4 x 4 On a coordinate plane, a graph of an image with a curve and straight line has 2 points. A closed circle appears at (negative 4, negative 2) and an open circle appears at (4, 5).Complete the inequality for the domain. −4 <= or < x <= or < 4
2 answers:
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Answer:
52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem:
Normal probability distribution:
Problems of normally distributed samples are 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
and standard deviation
In this problem, we have that:
What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct
This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So
X = 30732
By the Central Limit Theorem
has a pvalue of 0.7642.
X = 30054
has a pvalue of 0.2358
0.7642 - 0.2358 = 0.5284
52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct
Step-by-step
Population was 12.621 when it was measured
Next year it rose by 6%, so add that 6% to 100% and multiply with population measured
12.621 × (100%+6%) = 12.621 × 106% = 13.379,24
Since a man cant be 0,24, we count that as +1
13.379,24 = 13.379 + 1 = 13.380
That was for a year after measurement, now let's calculate for another year
Now, add those 6% to a new population number
13.380 × (100%+6%) = 13.380 × 106% = 14.182,8
since 0,8 isn't a man, instead we add again +1
14.182,8 = 14.182 + 1 = 14.183
now let's do it for another year after last, by adding those 6% to a newest population number
14.183 × (100%+6%) = 14.183 × 106% = 15.033,98
round it again to +1, since 0.98 isn't a man
15.033,98 = 15.033 + 1 = 15.034
that is it, now graph is in the picture.
Population was 12.621 when it was measured
Next year it rose by 6%, so add that 6% to 100% and multiply with population measured
12.621 × (100%+6%) = 12.621 × 106% = 13.379,24
Since a man cant be 0,24, we count that as +1
13.379,24 = 13.379 + 1 = 13.380
That was for a year after measurement, now let's calculate for another year
Now, add those 6% to a new population number
13.380 × (100%+6%) = 13.380 × 106% = 14.182,8
since 0,8 isn't a man, instead we add again +1
14.182,8 = 14.182 + 1 = 14.183
now let's do it for another year after last, by adding those 6% to a newest population number
14.183 × (100%+6%) = 14.183 × 106% = 15.033,98
round it again to +1, since 0.98 isn't a man
15.033,98 = 15.033 + 1 = 15.034
that is it, now graph is in the picture.