. Micah is cooking a pork roast for his family. He wants to be sure the pork roast has an internal temperature of at least 145 degrees Fahrenheit. He uses a thermometer to measure the internal temperature at three randomly chosen places. The minimum reading in the sample is 152 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic.
2. Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.
3. A population has μ = 80 and a standard deviation of σ = 5.2. What are the mean and standard deviation of the sampling distribution x̄ if a sample of 100 were taken?
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4. The amount of meat on a Subbies foot-long sub follows a Normal distribution, with a mean of 8 ounces and a standard deviation of 0.6 ounce. A random sample of 25 subs is selected every day and measured. What is the probability that the mean weight will exceed 8.2 ounces?
5. The average IQ score follows a Normal distribution, with a mean of μ = 100 and a standard deviation of σ = 15. What is the probability that the mean IQ score of 25 randomly selected people will be greater than 105?
6. Monogram Masters advertises on its website that 92% of customer orders are received within five working days. They performed an audit from a random sample of 200 of the 3,000 orders that month and it shows 175 orders were received on time. (10 points)Part A: Can we use a normal approximation? Explain. (5 points)Part B: If Monogram Masters customers really receive 92% of its orders within five working days, what is the probability that the proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less?
7. Carson’s tablet has 2,000 videos. The play time for the videos is skewed to the right, with a mean of 135 seconds and a standard deviation of 25 seconds. (10 points)Part A: Can you accurately calculate the probability that the mean play time is more than 142 seconds for an SRS of 10 videos? Explain. (4 points)Part B: If you take a random sample of 50 videos instead of 10, explain how the Central Limit Theorem allows you to find the probability that the mean play time is more than 142 seconds. Calculate this probability and show your work.
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