When Stephan moved from Illinois to Florida, his average monthly electric bill increased from $83 to $102. He is curious to know
1 answer:
Answer: The z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.
Step-by-step explanation:
Given: Average monthly electric bill in Illinois = $83
Average monthly electric bill in Florida = $102
Formula of z :
In Illinois, the mean monthly electric bill is $85, with a standard deviation of $3.20.
In Florida, the mean monthly electric bill is $105, with a standard deviation of $4.00.
Hence, the z-scores for Stephan's IL and FL electric bills. are -0.625 and 0.75 respectively.
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Answer:
.0228
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 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 normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
Find the probability that the average score of the 36 golfers exceeded 72.
This is 1 subtracted by the pvalue of Z when X = 72. So
By the Central Limit Theorem
has a pvalue of 0.9772
1 - 0.9772 = 0.0228