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 2.7 and standard deviation 0.80. (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 2.7 and 3.00? (Round your answers to four decimal places.) at most 3.00 between 2.7 and 3.00 (b) How large a sample size would be required to ensure that the first probability in part (a) is at least 0.99? (Round your answer up to the nearest whole number.) specimens You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a)for std error =std deviaiton/(n)1/2 =0.8/(25)1/2 =0.16

hence at most 3 =P(X<3) =P(X<3)=P(Z<(3-2.7)/0.16)=P(Z<1.875)=0.9696

between 2.7 and 3:00 =P(2.7<X<3.00)=P(0.5<Z<1.875)=0.9696-0.5 =0.4696

b)

for 0.99 percentile ; z =2.326

therefore corresponding std error =(X-mean)/z =(3-2.7)/2.326 =0.1290

therefore sample size =(std deviaiton/std error )2 =(0.8/0.1290)2 =~ 39

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