Given an infinite population with a mean of 75 and a standard deviation of 12,the probability that the mean of a sample of 36 observations,taken at random from this population,is less than 78 is:

A) 0.9332
B) 0.5987
C) 1.5000
D) None of these choices.

To find the probability that the sample mean is less than 78, we use the Z-score formula for a sample mean: Z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the given values: Z = (78 - 75) / (12/√36) = 3 / (12/6) = 3 / 2 = 1.5. Looking up 1.5 on the Z-table gives us the probability of 0.9332.