Specialist Mathematics · Unit 4 · Statistical inference · Sample means
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A production facility manufactures ball bearings with a mean diameter of \(50.0\) mm and a standard deviation of \(0.18\) mm. Quality control inspectors regularly select random samples of \(36\) bearings and measure their mean diameter. Which statement correctly describes the distribution of sample means?
The time spent by customers at a checkout in a supermarket is normally distributed with a mean of 4.2 minutes and a standard deviation of 1.8 minutes. A random sample of 25 customers is selected. (a) Calculate the standard error of the sample mean. (1 mark) (b) What is the probability that the mean time for this sample is less than 3.9 minutes? (1 mark)
A large population of test scores has a mean of μ = 72 and a standard deviation of σ = 8. A random sample of 25 students is taken from this population. (a) Determine the mean of the sampling distribution of the sample mean. (1) (b) Calculate the standard error of the mean, correct to 2 decimal places. (1) (c) Hence, determine the probability that the sample mean lies between 70 and 74, correct to 3 significant figures. (1)