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Answer:
66.98% probability that the mean gain for the sample was between 250 and 500.
Step-by-step explanation:
To solve this problem, it is important to know 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
, 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 mean gain for the sample was between 250 and 500?
This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 250.
So
X = 500
By the Central Limit Theorem
has a pvalue of 0.7257.
X = 250
By the Central Limit Theorem
has a pvalue of 0.0559.
So there is a 0.7257 - 0.0559 = 0.6698 = 66.98% probability that the mean gain for the sample was between 250 and 500.
The correlation coefficient (r) of the height and weight is 0.40391008.
Rounded, It will be 0.4
That means that the correlation between the height and weight is a positive weak correlation.
Rounded, It will be 0.4
That means that the correlation between the height and weight is a positive weak correlation.