SOLUTION: Please help...am so confused...taking stats online and have no teacher...thanks a bunch The diameters of grapefruits in a certain orchard are normally distributed with a mean of

Question 490332: Please help...am so confused...taking stats online and have no teacher...thanks a bunch
The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.44 inches and a standard deviation of 0.41 inches. Show all work.
(A) What percentage of the grapefruits in this orchard is larger than 5.36 inches?
(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.36 inches?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.44 inches and a standard deviation of 0.41 inches. Show all work.
(A) What percentage of the grapefruits in this orchard is larger than 5.36 inches?
---
z(5.36) = (5.36-5.44)/0.41 = -0.1951
P(x > 5.36) = P(z > -0.1951) = 0.5774
===============================================
(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.36 inches?
t(5.36) = (5.36-5.44)/[0.41/sqrt(100)] = -1.9512
---
P(x-bar > 5.36) = P(t > -1.9512 when df = 99) = 0.9731
================
Cheers,
Stan H.

RELATED QUESTIONS
Please help me with this.!!! The diameters of grapefruits in a certain orchard are... (answered by stanbon)

Cans of a certain beverage are labeled to indicate they contain 12 oz. The amounts in a... (answered by John10)

Help, The diameters of grapefruits in a certain orchard are normally distributed with... (answered by stanbon)

Please help...i am taking an online stats class and am so confused on this problem..I... (answered by stanbon)

I need HELP badly. The diameters of grapefruits in Jones Orchard are NORMALLY... (answered by ewatrrr)

The diameters of grapefruits in a certain orchard are normally distributed with a mean... (answered by stanbon)

PLEASE HELP ME IM BEGGING! IM having issues with thress question! 1.)Find the area... (answered by stanbon)

Please help..I have taking stats online and trying to teach myself...I am very confused... (answered by stanbon)