SOLUTION: I could use some help getting my thoughts and formulas together. Could you help me with this problem please. The diameters of apples in a certain orchard are normally distribute

Algebra ->  Probability-and-statistics -> SOLUTION: I could use some help getting my thoughts and formulas together. Could you help me with this problem please. The diameters of apples in a certain orchard are normally distribute      Log On


   

Question 626694: I could use some help getting my thoughts and formulas together. Could you help me with this problem please.
The diameters of apples in a certain orchard are normally distributed with a mean of 4.45 inches and a standard deviation of 0.42 inches. Show all work.
(A) What percentage of the apples in this orchard is larger than 4.38 inches?
(B) A random sample of 100 apples is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 4.38 inches?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The diameters of apples in a certain orchard are normally distributed with a mean of 4.45 inches and a standard deviation of 0.42 inches. Show all work.
(A) What percentage of the apples in this orchard is larger than 4.38 inches?
z(4.38) = (4.38-4.45)/0.42 = -0.17
P(x > 4.38) = P(z > -0.17) = normalcdf(-0.17,100) = 0.5662 = 56.62%
=========================================================================

(B) A random sample of 100 apples is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 4.38 inches?
z(4.38) = (4.38-4.45)/[0.42/sqrt(100)) = -1.67
----
P(x-bar > 4.38) = P(z > -1.67) = normalcdf(-1.67,100) = 0.9525 = 95.25%
========================
Cheers,
Stan H.
===========================