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Lerok [7]
3 years ago
15

A video club wants to reward its best members with a discount based on the member’s number of movie rentals and the number of ne

w members referred by the member. The discount is in percent and is equal to the sum of the rentals and the referrals, but it cannot exceed 75 percent. (Hint: Math.min.) Write a program DiscountCalculator to calculate the value of the discount.
Mathematics
1 answer:
ivanzaharov [21]3 years ago
8 0

Answer:

public class MovieRental

{

public static void main(String[] args)

{

 Scanner in = new Scanner(System.in);

 

 System.out.print("Enter the number of movie rentals: ");

 int movieRentals = in.nextInt();

 

 System.out.print("Enter the number of members referred to the video club: ");

 int memberReferral = in.nextInt();

 

 in.close();

 

 double discountVal = Math.min(movieRentals + memberReferral, 75);

 

 System.out.println("The discount is equal to: " + discountVal);

}

}

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Answer:

a) P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)

And we can find this probability using the complement rule:

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b) P(X

And we can find this probability uing the normal standard table:

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And we can find this probability with this difference:

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And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-1.25

Step-by-step explanation:

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".  

Part a

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

X \sim N(5,1.2)  

Where \mu=5 and \sigma=1.2

We are interested on this probability

P(X>3.5)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)

And we can find this probability using the complement rule:

P(z>-1.25)=1-P(z

Part b

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability uing the normal standard table:

P(z

Part c

P(3.5

And we can find this probability with this difference:

P(-1.25

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-1.25

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