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spr10_ex1asol

# spr10_ex1asol - STA 4322/5328 Spr/2010 Mini Exam1 PRINT...

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STA 4322/5328 – Spr/2010 Mini Exam1 PRINT NAME _______________ For all problems, the sample mean, sample variance, and sample proportion are: ( 29 ) , ( ~ where : Proportion Sample 1 1 : variance Sample 1 : Mean Sample ^ 1 2 1 p n Bin Y n Y p Y Y n- Y n Y n i i n i i = - = = = Q.1 : A spectrometer gives readings that are normally distributed with mean equal to the true weight if the object being measured, and a standard deviation of 0.6. Assume repeated measurements are independent. P1.a. If a lab technician makes 9 readings of the spectrometer on a particular item, what is the sampling distribution of the sample mean, the average of the 9 readings? Label the true weight as Y*. = = = 040 . 0 9 6 . 0 *, ~ 2 2 Y Y Y N Y σ μ P1.b. What is the probability that the sample mean will lie within 0.3 of the true mean? ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 8664 . ) 4332 (. 2 ) 0668 . 0 5 . 0 ( 2 5 . 1 5 . 0 2 5 . 1 5 . 1 040 . 0 3 . 0 * 040 . 0 3 . 0 3 . 0 * 3 . 0 = = - = - = - = - - = - - Z P Z P Y Y P Y Y P Y σ P1.c.

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spr10_ex1asol - STA 4322/5328 Spr/2010 Mini Exam1 PRINT...

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