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lina2011 [118]
3 years ago
11

g If a random sample of 18 deliveries was selected instead and the standard deviation of these delivery times was found to be 9.

31 minutes, find the probability that their average delivery time is between 21 and 25 minutes
Mathematics
1 answer:
lana [24]3 years ago
6 0

Answer:

We can use the z score formula given by:

z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

If we use this formula we got:

z=\frac{21-20}{\frac{9.31}{\sqrt{18}}}= 0.456

z=\frac{25-20}{\frac{9.31}{\sqrt{18}}}= 2.279

And using a calculator, excel or the normal standard table and we have that:

P(0.456

Step-by-step explanation:

We assume this previous info:  It is known that the amounts of time required for room-service delivery at a certain Marriott Hotel are Normally distributed with the average delivery time of 20 minutes.

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the delivery times of a population, and for this case we know the distribution for X is given by:

X \sim N(20,9.31)  

Where \mu=20 and \sigma=9.31

Since the distribution for X is normal then the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we can use the z score formula given by:

z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

If we use this formula we got:

z=\frac{21-20}{\frac{9.31}{\sqrt{18}}}= 0.456

z=\frac{25-20}{\frac{9.31}{\sqrt{18}}}= 2.279

And using a calculator, excel or the normal standard table and we have that:

P(0.456

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Two arithmetic means between 3 and 24 are -
defon

The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

<h3>What is arithmetic mean?</h3>

Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.  

The two arithmetic means between 3 and 24 are has to be inserted.

3, A₂, A₃, 24

All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:

t(n)=a(n-1)d

Here, d is the common difference a is the first terms and n is the total term.  The first term, a=3 and t₄=24. Thus, the common difference is;

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Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.

Learn more about the arithmetic mean here;

brainly.com/question/14831274

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