Question

Problems 1 and 2, draw the appropriate probability distribution curve and label all values. Show all your work. Do not use Excel or a statistical calculator to compute the probabilities. Showing only the answer will result in a zero grade.

1. Whitney Gourmet Cat Food has determined the weight of their cat food can is normally distributed with a mean of 3 ounces and a standard deviation of 0.05 ounces. To meet legal and customer satisfaction goals each can must weigh between 2.95 and 3.1 ounces.
   1. If a single can is chosen, what is the probability it will weigh less between 2.95 and 3.1 ounces?
      
      
      
      
      
      

1. 2. If 5 cans are chosen, what is the probability the sample mean will be less than 2.95 ounces?
      
      
      
      
      
      
      
      
      
   3. If 5 cans are chosen, there is a 95 percent probability the sample mean will fall between what two values symmetrically distributed around the population mean?
      
      
      
      
      
      
      
      
      
      
2. Lightning Speed manufactures carbon fiber composite tubing for bicycles. This is a mature process and the population mean for their tubing’s strength is known to be 318 hundred pounds per square inch (k lbs) and the population standard deviation is known to be 20 k lbs.
   
   
   1. If 30 pieces of tubing are sampled and tested, what is the probability the sample mean is greater than 320 k lbs?
      
      
      
      
      
      
      

2. Use of the standard normal distribution table requires the sampling distribution of the mean to be normally distributed.   If the population is not known to be normally distributed, how can you be sure the sampling distribution of the mean is normally distributed? Provide sufficient detail to justify your answer.
   

Problems 3-5, use the appropriate equations as shown in your text. Show all your work. Do not use Excel or a statistical calculator to compute probabilities. Showing only the answer will result in a zero grade.

3. A published poll has indicated that 1 out of 15 people who use regular gasoline will pay $.40/gallon more for regular gasoline without ethanol.
   
   1. A local service station sells both regular grade gasoline with ethanol and regular grade gasoline without ethanol. What is the probability that the 20^th person visiting the service station to purchase regular gasoline will be the 4th person to purchase regular gasoline without ethanol?
      
      
      
      
      

2. If 20 people visit the service station to purchase regular gasoline, what is the probability that at least two will purchase regular gasoline without ethanol?
   
   
   
   
   

4. A published poll has indicated that 1 out of 20 people will pay 15% more for Spotted Cow brand of milk that is organic as compared to Spotted Cow brand of milk that is not organic. Fifty people are surveyed and ask if they would pay 15% more for Spotted Cow organic milk as compared to Spotted Cow milk that is not organic.
   
   What is the probability that the first person surveyed will indicate he or she is willing to pay 15% more for Spotted Cow organic milk?
   
   
   
   
5. A lottery is conducted in which 7 winning numbers are randomly selected from a total of 62 numbers (1-62). In addition, the Powerball, a single winning number, is selected from an independent pool of 26 numbers (1-26). You select 7 numbers from the pool of 62 numbers.
   
   1. What is the probability that you selected 4 winning numbers?
      
      
      
      
      
      
      
      
   2. What is the probability that you selected none of the winning numbers?
      
      
      
      
      
      
      
      
      
      
   3. What is the probability that you will select at least one of the winning numbers?
      
      
      
      
      
      
      
      
      
   4. If the probability of choosing 2 of the 7 winning numbers from the pool of 62 numbers is .08862, what is the probability will choose the Powerball from the pool of 26 numbers?
      
      

Answer 1