Sarah found the mean of a set of numbers to be 205.09.how should she read this value out loud?
2 answers:
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Answer:
86.64% probability that the mean tire life of these four tires is between 57,000 and 63,000 miles
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:
Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles
This is the pvalue of Z when X = 63000 subtracted by the pvalue of Z when X = 57000. So
X = 63000
By the Central Limit Theorem
has a pvalue of 0.9332
X = 57000
has a pvalue of 0.0668
0.9332 - 0.0668 = 0.8664
86.64% probability that the mean tire life of these four tires is between 57,000 and 63,000 miles