16. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 miles per gallon and a standard deviation 3.5 miles per gallon
What is your question?
16. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 miles per gallon and a standard deviation 3.5 miles per gallon.
a) What is the probability that randomly selected Cobalt gets more than 34 miles per gallon?
The answer is approximately =0.017
b) Ten Cobalts are randomly selected and the miles per gallon for each car are recorded. What is the probability that the mean miles per gallon exceed 34 miles per gallon?
The final answer will be = 0.0351
c) Twenty Cobalts are randomly selected and the miles per gallon for each car are recorded, What is the probability that the mean miles per gallon exceeds 34 miles per gallon? Would this result be unusual? Explain.
The sample mean obtained is unusual.
17. Burger King's Drive-Through: Suppose that cars arrive at Burger King's drive-through at the rate of 20 cars every hour between 12:00 noon and 1:00 PM. A random sample of 40 one-hour time periods between 12:00 noon and 1:00 P.M. is selected and has 22.1 as the mean number of cars arriving.
How did you find part a?
14
To answer questions related to the Chevrolet Cobalt's miles per gallon in highway driving, which is normally distributed with a mean of 32 miles per gallon and a standard deviation of 3.5 miles per gallon, we can use statistical concepts and calculations.
Let's say we have a specific question, like "What is the probability of getting at least 35 miles per gallon in highway driving?" Here's how you can find the answer:
Step 1: Determine the Z-score
- The Z-score is a standard score that indicates how many standard deviations an observation is from the mean.
- It is calculated using the formula: Z = (X - μ) / σ, where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
- In this case, X = 35, μ = 32, and σ = 3.5.
Step 2: Find the probability using the Z-table
- The Z-table is a tool that provides the area under the standard normal curve (a bell-shaped curve with a mean of 0 and a standard deviation of 1) for a given Z-score.
- You need to look up the Z-score in the Z-table to find the probability.
- In our example, we already calculated the Z-score as follows:
Z = (35 - 32) / 3.5 = 0.857
Now, we need to find the area to the left of this Z-score in the Z-table.
- If you're using a printed Z-table, find the row corresponding to the first digit of the Z-score (0.8) and the column corresponding to the second digit (0.05). The intersection of this row and column gives you the area under the curve.
- If you're using an online Z-table or calculator, input the Z-score and it will provide you with the probability directly.
Step 3: Calculate the probability
- Once you find the Z-score in the Z-table, it will give you the probability associated with that Z-score.
- Suppose the Z-table gives you a probability of 0.8051 for a Z-score of 0.857 (this is just an example).
- However, we're interested in finding the probability of getting at least 35 miles per gallon, which means the area to the left of 35 needs to be calculated.
- Since we have a normal distribution, we know the area to the left of 35 is equal to 1 minus the area to the right of 35.
Step 4: Calculate the final probability
- Subtract the probability you found in Step 3 from 1 to get the final probability.
In this case, if you find that the probability of getting at least 35 miles per gallon is 0.8051 (using the Z-table as an example), the final probability would be:
Final Probability = 1 - 0.8051 = 0.1949 (or 19.49%)
By following these steps, you can use the given mean and standard deviation to calculate the probability of other scenarios or answer different questions related to the miles per gallon in highway driving for the Chevrolet Cobalt.