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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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A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in
Mars2501 [29]

Answer:

For this case we want to determine if  there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66 (a;ternative hypothesis) and then the system of hypothesis are:

Null hypothesis: p \leq 0.66

Alternative hypothesis: p >0.66

And the estimated proportion for this case would be:

\hat p =\frac{X}{n} = \frac{1020}{1500}=0.68

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to determine if  there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66 (a;ternative hypothesis) and then the system of hypothesis are:

Null hypothesis: p \leq 0.66

Alternative hypothesis: p >0.66

And the estimated proportion for this case would be:

\hat p =\frac{X}{n} = \frac{1020}{1500}=0.68

4 0
3 years ago
Bryan needs to finish a book for
Galina-37 [17]

Answer:

22.5 pages per week

Step-by-step explanation:

Considering that After 2 weeks, he has read

45 pages, and after 6 weeks, he has

read 135 pages

Difference in weeks = 6-2=4 weeks

Difference in pages=135-45=90

Rate per week will be 90÷4=22½ pages per week

To prove this

If 1 week is 22½

2 weeks will be 2*22½=45

6 weeks will be 6*22½=135

Therefore, the reading rate is 22.5 or 22½ pages per week

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11 and 12 and the work plsss
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Answer:

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Step-by-step explanation:

5 0
3 years ago
14feet 23feet round each measurement to the nearest ten
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3 0
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Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate
sertanlavr [38]

The monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.

Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.

A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).

Monthly Payments

Option 1

Loan Amount = $200,000

Number of payments = 30×12 = 360

Monthly interest rate = 10%/12 = 0.008333333

Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]

Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]

Monthly payment=33062.328/18.83739

Monthly payment=$1755.144

Option 2

Loan Amount = $200,000

Number of payments = 15 x 12=180

Monthly interest rate = 9.5%/12=0.00792

Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]

Monthly payment=6553.096/3.137

Monthly payment=$2088.97

Total Payments

Option 1

As we've found out the monthly payments, we now need to multiply it by the number of months.

$1755.144×360 = $631851.84

Option 2

$2088.97×180 = $376014.6

Conclusion

Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.

Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.

Learn more about monthly cost from here brainly.com/question/1476828.

#SPJ1

5 0
2 years ago
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