Reference no: EM132322692
Assignment - Basic Statistics Questions
Need assistance with the statistics questions given below.
Q1. Use the z-table to find the requested probabilities. Enter your answers to 4 decimal places.
(a) P(z < 2.4)
(b) P(z ≥ 1.74)
(c) P(-2.88 < z < 1.75)
Q2. If P(z < z*) = 0.25, then z* is which of the following?
- less than zero
- greater than zero
Q3. Speeding: On a stretch of Interstate-89, car speed is a normally distributed variable with a mean of 67.7 mph and a standard deviation of 3.3 mph.
Suppose you are a police officer on this stretch of road and only have time to ticket 1% of the cars that go by you. How fast should someone be traveling before you pull them over? Round your answer to 1 decimal place.
Q4. Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.9 pounds.
(a) Suppose you only want to keep fish that are in the top 10% as far as weight is concerned. What is the minimum weight of a keeper? Round your answer to 2 decimal places.
(b) Suppose you want to mount a fish if it is in the top 0.5% of those in the lake. What is the minimum weight of a bass to be mounted? Round your answer to 2 decimal places.
(c) Determine the weights that delineate the middle 95% of the bass in Clear Lake. Round your answers to 2 decimal places.
Q5. Potatoes: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 9 ounces and a standard deviation of 1.1 ounces. Round your answers to 4 decimal places.
(a) If one potato is randomly selected, find the probability that it weighs less than 10 ounces.
(b) If one potato is randomly selected, find the probability that it weighs more than 12 ounces.
(c) If one potato is randomly selected, find the probability that it weighs between 10 and 12 ounces.
Q6. Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 1.9 pounds and a standard deviation of 0.6 pounds.
(a) If you catch one random bass from Clear Lake, find the probability that it weighs less than 1 pound? Round your answer to 4 decimal places.
(b) If you catch one random bass from Clear Lake, find the probability that it weighs more than 3 pounds? Round your answer to 4 decimal places.
(c) If you catch one random bass from Clear Lake, find the probability that it weighs between 1 and 3 pounds? Round your answer to 4 decimal places.
Q7. Bass - Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 2.2 pounds and a standard deviation of 0.6 pounds. Suppose you catch a stringer of 6 bass with a total weight of 16.4 pounds. Here we determine how unusual this is.
(a) What is the mean fish weight of your catch of 6? Round your answer to 1 decimal place.
(b) If 6 bass are randomly selected from Clear Lake, find the probability that the mean weight is greater than the mean of those you caught. Round your answer to 4 decimal places.
(c) Which statement best describes your situation?
- This is not particularly unusual because the mean weight of your fish is only 0.5 pounds above the population average.
- This is unusual because the probability of randomly selecting 6 fish with a mean weight greater than or equal to the mean of your stringer is less than the benchmark probability of 0.05.
Q8. Bass - Samples: The bass in Clear Lake have weights that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.9 pounds.
(a) If you catch 3 random bass from Clear Lake, find the probability that the mean weight is less than 1.0 pound. Round your answer to 4 decimal places.
(b) If you catch 3 random bass from Clear Lake, find the probability that the mean weight it is more than 3 pounds. Round your answer to 4 decimal places.
Q9. Potatoes - Samples: Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 7.8 ounces and a standard deviation of 1.1 ounces.
(a) If 4 potatoes are randomly selected, find the probability that the mean weight is less than 8.9 ounces. Round your answer to 4 decimal places.
(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 8.7 ounces. Round your answer to 4 decimal places.
Q10. Potatoes - Samples: Assume the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.2 ounces. He bags his potatoes in groups of 6. You buy a bag and the total weight is 42 ounces. Here we determine how lucky or unlucky you are.
(a) What is the mean potato weight in your bag of 6? Enter your answer to 1 decimal place.
(b) If 6 potatoes are randomly selected, find the probability that the mean weight is less than the mean found in your bag. Round your answer to 4 decimal places.
(c) Which statement best describes your situation?
- You got lucky with such a generous amount of potato your bag.
- You got extremely unlucky because the probability of getting a bag weighing less than yours is about 0.01%.
- This is an unusually small amount of potatoes. You are unlucky because the probability of getting a bag weighing less than yours is only about 2.1%.
- This is not particularly unusual because the mean weight in your bag is only 1 ounce below the mean of all Carl's potatoes.