Consider the following data:

x 4 5 6 7 8

P(X=x) 0.1 0.3 0.1 0.2 0.3

Step 1 of 5: Find the expected value E(X). Round your answer to one decimal place.

Step 2 of 5:

Find the variance. Round your answer to one decimal place.

Step 3 of 5:

Find the standard deviation. Round your answer to one decimal place.

Step 4 of 5:

Find the value of P(X>6)P(X>6). Round your answer to one decimal place.

Step 5 of 5:

Find the value of P(X≥8)P(X≥8). Round your answer to one decimal place.

A random sample of 36 mid-sized cars tested for fuel consumption gave a mean of 26.4 miles per gallon with a standard deviation of 2.3 miles per gallon. Find a 99% confidence interval for the true population mean miles per gallon. Upload the file with your answer and work.  

Problem 16-03

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
   
   
   
2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
   
   
   
3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.
   
   miles

Aircraft companies had very difficult times during the pandemic period. AHL, and OA have created some advantages for their loyal customers, especially for the Istanbul-Ankara flight. AHLprovides 900 points (flight miles) for each flight to its customers flying from Istanbul to Ankara. However, it gives 1000 (flight miles) extra points to more than 3 flights and 1350 (flight miles) to more than 6 flights within three months. While OA gives 1200 points (flight miles) for each flight, it gives 1500 (flight miles) extra points for every 5 flights within three months. While the ticket price of AHL company in Istanbul-ankara is 800 TL, the ticket price of OA is 600 TL.

For a person who wants to make an Istanbul-ankara flight 60 times in the next twelfe months, please create an integer programming model to maximize flight miles.

The average number of miles driven on a full tank of gas in a certain model car before its​ low-fuel light comes on is 341. Assume this mileage follows the normal distribution with a standard deviation of 39 miles. Must show ALL calculations by use of formulas ONLY, no Excel use.

Complete parts a through d below.

a. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel less than 369 miles on the next tank of​ gas?

b. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel more than 248 miles on the next tank of​ gas?

c. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel between 259 and 279 miles on the next tank of​ gas?

d. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel exactly 279 miles on the next tank of​ gas?

Problem 16-03

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
   
   
   
2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
   
   
   
3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.
   
   miles

A tire manufacturer believes that the tread life of its snow tires can be described by Normal model with a mean of 32,000 miles and a standard deviation of 2500 miles.

a). If you buy a set of these tires, would it be reasonable for you to hope that they'll last 40,000 miles? Explain.

b). Approximately what fraction of these tires can be expected to last less that 30,000 miles?

c). Approximately what fraction of these tires can be expected to last between 30,000 and 35,000 miles?

d). Estimate the IQR for these data.

e). Im planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer does not want to take too big a risk. If the dealer is willing to give refunds to no more than 1 of every 25 customers, for what mileage can he guarantee these tires to last?

Problem 16-03

Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
   
   
   
2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
   
   
   
3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.
   
   miles

1. Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles. Management also believes that the standard deviation is 5000 miles and that tire mileage is normally distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach 30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000 miles, Grear will refund a customer $1 per 100 miles short of 30,000.

   1. For each tire sold, what is the expected cost of the promotion? If required, round your answer to two decimal places.
      
      
      
   2. What is the probability that Grear will refund more than $50 for a tire? If required, round your answer to three decimal places.
      
      
      
   3. What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00? If required, round your answer to the hundreds place.
      
      miles

11. How can a hotel take a proactive stance on fire safety?