Suppose the sediment density (g/cm) of a randomly selected specimen from a certa

Question

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.63 and standard deviation 0.79. (a If a randorm sample of 25 specimens is selected, what is the probabilt that the sample average sediment density (Round your answers to four decimal places.) at most 3.00 between 2.63 and 3.00 at most 3.00, Between a 53 ao? (b) How large a sample size would be required to ensure that the probability in part (a) is at least 0.992 (Round your answer up to the nearest whole number.) specimens

Explanation / Answer

= 2.63 = 0.79

(a) n = 25

P(x' <= 3.00)

=> P(z <= (3.00 - 2.63) / 0.79 * 25)

= P(z <= 2.3418)

= 0.9904.

P(2.63 <= x' <= 3.00)

= 0.9904 - 0.5

= 0.4904.

(b) Using z tables,

p >= 0.99 => z >= 2.3263

=> x' >= 2.63 + 2.3263 * 0.79 / 25

=> x' >= 2.9976 = 3 specimens.

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