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Ivenika [448]
3 years ago
5

PLEASE HELP ME FAST!!!

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
3 0

Answer:

16,7

Step-by-step explanation:

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Fill in the blank. In a drive thru performance study, the average service time for McDonald's is 203.21 seconds with a standard
Alenkasestr [34]

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 \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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 \mu = 203.21, \sigma = 5.67

Sample of 90

This means that n = 90, s = \frac{5.67}{\sqrt{90}} = 0.59767

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.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

0.025 = \frac{X - 203.21}{0.59767}

X - 203.32 = 0.025*0.59767

X = 203.35

203.35 seconds.

3 0
3 years ago
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