by BlastRoom
Checking the conditions and finding the probability that a sample mean falls in a range.
#probability_and_statistics

20 questions
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A dairy fills bottles with population mean mu = 750 mL and sigma = 18 mL. Random samples of 9 bottles are taken and x-bar is recorded. What are the mean and standard deviation of the sampling distribution of x-bar?
Rechargeable batteries have population mean mu = 10.0 hours and sigma = 1.6 hours. A lab records x-bar for random samples of 16 batteries. What are the center and standard deviation of the sampling distribution of x-bar?
A cereal line fills boxes with population mean mu = 500 g and sigma = 30 g. Random samples of 25 boxes are weighed, and x-bar is recorded. What are the mean and standard deviation of the sampling distribution of x-bar?
Medical tablets have population mean thickness mu = 3.2 mm and sigma = 0.20 mm. Random samples of 4 tablets are measured. What are the mean and standard deviation of the sampling distribution of x-bar?
Train commute times have population mean mu = 42 min and sigma = 12 min. Random samples of 36 trips are taken, and x-bar is recorded. What are the mean and standard deviation of the sampling distribution of x-bar?
At a clinic, patient wait times have mu = 18 min and sigma = 6 min. For random samples of 9 patients, the sampling distribution of x-bar has standard deviation 2 min. If x-bar = 21 min, what is its z-score?
A juice filler has mu = 355 mL and sigma = 8 mL. For random samples of 16 bottles, x-bar has standard deviation 2 mL. If one sample has x-bar = 351 mL, what is the z-score?
In a district, algebra exam scores have mu = 72 points and sigma = 10 points. For random samples of 25 students, x-bar has standard deviation 2 points. A sample has x-bar = 75. What z-score corresponds to this sample mean?
Greenhouse plant heights have mu = 40 cm and sigma = 12 cm. For random samples of 36 plants, x-bar has standard deviation 2 cm. If a sample has x-bar = 37 cm, what is the z-score?
A bakery's roll masses have mu = 100 g and sigma = 15 g. For random samples of 25 rolls, x-bar has standard deviation 3 g. To four decimals, what is P(x-bar is greater than 106 g)?
Reaction times have mu = 500 ms and sigma = 40 ms. The curve is the sampling distribution of x-bar for samples of 16 (SD 10 ms). The red lines mark 485 ms and 515 ms. To four decimals, what is the probability that x-bar is in the shaded region?

Bottles of water from a filler have mu = 2.50 L and sigma = 0.20 L. For random samples of 16 bottles, x-bar has standard deviation 0.05 L. To four decimals, what is P(x-bar is less than 2.42 L)?
Bean plants in a greenhouse have mu = 64 cm and sigma = 12 cm. For random samples of 36 plants, x-bar has standard deviation 2 cm. To four decimals, what is P(x-bar is between 62 cm and 68 cm)?
Bus trip times have mu = 80 min and sigma = 20 min. The curve is the sampling distribution of x-bar for samples of 25 trips (SD 4 min). The red line marks 72 min. To four decimals, what is the probability that x-bar is in the shaded region?

Vitamin tablets from a factory have mu = 120 mg and sigma = 30 mg. For random samples of 9 tablets, x-bar has standard deviation 10 mg. To four decimals, what is P(x-bar is between 110 mg and 130 mg)?
Incubator temperatures have mu = 38.0 °C and sigma = 4.0 °C. For random samples of 64 readings, x-bar has standard deviation 0.5 °C. To four decimals, what is P(x-bar is less than 37.0 °C)?
The histogram shows a farm's population of egg masses, with mu = 62 g and sigma = 5 g. A random sample of 8 eggs is used to compute x-bar. Is a normal model for x-bar defensible, and why?

The histogram shows the population of clinic bill amounts, with mu = $80 and sigma = $60. A random sample of 12 bills is used to compute x-bar. Is a normal model for x-bar defensible, and why?

The histogram shows the population of bolt lengths from a factory, with mu = 50 mm and sigma = 3 mm. A random sample of 64 bolts is used to compute x-bar. Is a normal model for x-bar defensible, and why?

The histogram shows the population of delivery package masses, with mu = 4.0 kg and sigma = 6.0 kg. A random sample of 20 packages is used to compute x-bar. Is a normal model for x-bar defensible, and why?

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Margin of Error: What Changes It
40 questions