posted by Michael on .
The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.52 inches and a standard deviation of 0.46 inches
(A) What percentage of the grapefruits in this orchard is larger than 5.45 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 5.45 inches
Z = Z score found in standard normal distribution tables
X = value of random variable, the diameter of 5.45 inchs
μ = mean diameter of population, 5.52 inches
σ = standard deviation of population, 0.46 inch.
Look up a standard normal distribution, which is usually given in percentage of population less than the Z-score, i.e. left tail (but check if this is the case).
What you need is the right tail, i.e. percentage of population greater than the Z-score. To get this from the table, subtract the left tail from ONE to get the right-tail.