Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
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 [tex]\mu = 203.21, \sigma = 5.67[/tex]
Sample of 90
This means that [tex]n = 90, s = \frac{5.67}{\sqrt{90}} = 0.59767[/tex]
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.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.025 = \frac{X - 203.21}{0.59767}[/tex]
[tex]X - 203.32 = 0.025*0.59767[/tex]
[tex]X = 203.35[/tex]
203.35 seconds.
