Question

28. Sun Love grapefruit growers have determined that the diameters of the grapefruits are
normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches. Which
quantity is greater, or are they the same?
Quantity A: The probability that a single randomly selected grapefruit will have a
diameter of at least 4.14 inches
Quantity B: The probability that the sample mean diameter of a random sample of 35
grapefruits will be at least 4.14 inches .
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the given information.

Answer 1

For Quantity A Define the standard random variable Z as X denotes diameter

Then using normal table we have

For Quantity B Define the standard random variable Z as   denotes mean diameter

Then using normal table we have

Hence the correct option is B. Quantity B is greater.