Suppose the sediment density gcm of a randomly selected...

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean and standard deviation (suggested in “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants,” Water Research, 1984: 1169–1174). If a random sample of specimens is selected, what is the probability that the sample average sediment density is at most ? Between and ? How large a sample size would be required to ensure that the first probability in part (a) is at least ?

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00:01 Here the question says that suppose the sediment density of a random selected specimen for a certain reason is normally distributed with mean 2 .65 and a standard deviation of 0 .85.

00:13 In modeling sediment and water column intersection for hydropobic pollutant, water research, 1984 to 1169 to 1174.

00:24 So first we have to find a random sample of 25 specimen is selected.

00:29 What is the probability that the sample average sediment density is at most 3 between 2 .65 and 3 .0 and b how large a sample size would be required to ensure that the first probability in part a is at least 0 .99.

00:45 So here the concept and the reason which is used is normal distribution which is a continuous distribution and important statistics are often used in the natural and the social science to represent.

00:59 Represent real value random variable whose distribution are not known and the standard normal distribution is a type of normal distribution with mean equal to zero and standard deviation is equals to one by here we use the formula of z score for the sample mean which is known as z is equals to x minus mu by sigma divided by square root of n so now moving towards the solution here the sediment density is normally distributed with mean me mu is equals to 2 .65 and the standard deviation is the standard deviation is equals to 0 .85 so now moving towards part a here if the random sample of 25 specimens is selected then the probability that the sample average sediment density is at most 3 is first we have to find the standard deviation of mean sediment density the standard deviation of mean sediment density density is sigma x is equals to 0 .85 whole divided by square root of 25 which is equals to 0 .85 divided by 5 is equal to 0 .17.

03:13 Now now the probability p x bar is less than equals to 3 is equal to p z less than equals to 3 minus 2 .65 divided by 0 .17, which is equals to p...

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