document.write( "Question 366226: The diameters of peaches in a certain orchard are normally distributed with a mean of 3.85 inches and a standard deviation of 0.42 inches. Show all work.
\n" ); document.write( "(A) What percentage of the peaches in this orchard is larger than 3.79 inches?
\n" ); document.write( "(B) A random sample of 100 peaches is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 3.79 inches?
\n" ); document.write( "

Algebra.Com's Answer #260969 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
The diameters of peaches in a certain orchard are normally distributed with a mean of 3.85 inches and a standard deviation of 0.42 inches. Show all work.
\n" ); document.write( "------------------------
\n" ); document.write( "(A) What percentage of the peaches in this orchard is larger than 3.79 inches?
\n" ); document.write( "z(3.79) = (3.79-3.85)/0.42 = -0.1429
\n" ); document.write( "P(x > 3.79) = P(z > -0.1429) = 0.5568
\n" ); document.write( "-----------------------------------------\r
\n" ); document.write( "\n" ); document.write( "(B) A random sample of 100 peaches is gathered and the mean diameter is calc
\n" ); document.write( "ulated. What is the probability that the sample mean is greater than 3.79 inches?
\n" ); document.write( "z(3.79) = (3.79-3.85)/[0.42/sqrt(100)] = -1.4286
\n" ); document.write( "P(x-bar > 3.79) = P(-1.4286,100) = 0.9234
\n" ); document.write( "======================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "
\n" );