On January 22 in 1943, the town of Spearfish, South Dakota, set the record for the world’s fastest temperature change. At 7:30 a
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Answer:
Step-by-step explanation:
To solve this question, we have to know what a z-score is and the central limit theorem.
Z-score:
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 z-score corresponding to a sample mean of M = 76?
This is Z when X = 76. So
By the Central Limit Theorem