the volume of a triangular prism is increased by a factor of 8. By what factor is the surface area increased?
1 answer:
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Answer:
0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct
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 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
, the sample means with size n of at least 30 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 be less than 48,101 miles in a sample of 281 tires if the manager is correct?
This is the pvalue of Z when X = 48101. So
By the Central Limit Theorem
has a pvalue of 0.0091
0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct
Answer:
(B) Time (min) 2 , 3 , 7 , 9
Temperature (°C) 60.6 , 64.3 , 79.1 , 86.5
Step-by-step explanation:
The rate of change is found by using the formula for slope:
For option A, this gives us
m =(64.4-61.0)/(3-2) = 3.4/1 = 3.4
This is not more than relationship A.
For option B, we have
(64.3-60.6)/(3-2) = 3.7/1 = 3.7
This is more than relationship A.
For option C, we have
(65.3-61.8)/(3-2) = 3.5/1 = 3.5
This is not more than relationship A.
For option D, we have
(64.6-61.0)/(3-2) = 3.6/1 = 3.6
This is not more than relationship A.