Train A and train B leave the station at 2 pm. The graph below shows the distance covered by the two trains. Compare the two spe
eds of the two trains. Show your work !
1 answer:
Both trains travel for 7 time units.
Train A travels 385 distance units, so its speed is
Train B travels 577.5 distance units, so its speed is
Note that the units are not specified, but considering that we're talking about trains, the graph is likely to be showing distance in km (or miles) and time in hours.
Also, the distance traveled by train B is not perfectly aligned with the grid, so I assumed that it was the average between the two ticks of 550 and 605.
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Answer:
68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50
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, which is also called standard error
In this problem, we have that:
What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50
This is the pvalue of Z when X = 1000+50 = 1050 subtracted by the pvalue of Z when X = 1000-50 = 950. So
X = 1050
By the Central Limit Theorem
has a pvalue of 0.8438
X = 950
has a pvalue of 0.1562
0.8438 - 0.1562 = 0.6876
68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50