Miguel wrote the predicted and residual values for a data set using the line of best fit y = 1.82x – 4.3. He left out two of the
values.
1 answer:
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Answer:
5) 203.35
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
The average service time for McDonald's is 203.21 seconds with a standard deviation of 5.67 seconds.
This means that
Sample of 90
This means that
There is a 51% chance that the average drive-thru service time is less than ________ seconds.
X when Z is in the 51st percentile, that is, has a p-value of 0.51, so X when Z = 0.025.
By the Central Limit Theorem
203.35 seconds.