uppose the sediment density (g/cm) of a randomly selected specimen from a certai

Question

uppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.63 and standard deviation 0.75. (a) If a random sample of 25 specimens is selected, what is the probability that the sample average sediment density is at most 3.00? Between 2.63 and 3.00? (Round your answers to four decimal places.) at most 3.00 between 2.63 and 3.00 (b) How large a sample size would be required to ensure that the probability in part (a) is at least 0.99? (Round your answer up to the nearest whole number.) specimens

Explanation / Answer

answer

population mean = 2.63

Standard Deviation= .75
n = 25

so, we go to our formula:

(score - mean)/sd = z

(3.00 - 2.63) / sd = z

what is the standard deviation of the mean? I TOLD you there were many standard deviations. Pay attention. :) it is

sd(pop)/sqrt(n) = .75 /sqrt(25) = .75 / 5 = 0.15

(3.00 - 2.63) / .15 = z

.37 / .15 = z
2.46 = z

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