Obtain the total salary?)
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Answer:
64.76% probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams
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 mean weight of the sample babies would differ from the population mean by less than 40 grams
This is the pvalue of Z when X = 3242 + 40 = 3282 subtracted by the pvalue of Z when 3242 - 40 = 3202
X = 3282
By the Central Limit Theorem
has a pvalue of 0.8238.
X = 3202
has a pvalue of 0.1762
0.8238 - 0.1762 = 0.6476
64.76% probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams
The mean is found by dividing the sum of all terms by the number of terms present in the set.
Set up the equation:
The mean of this sequence is 5.
Set up the equation:
The mean of this sequence is 5.