The mean weight of loads of rock is 47.0 tons with a standard deviation of 6.0 tons. If 16 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 46.2 tons. Assume that the variable is normally distributed.
A) 21.23
B) 28.77
C) 71.23
D) 78.77

Question

Quizplus · Accepted Answer

The sample size n = 16 is greater than 30 and the population standard deviation σ= 6. Therefore, we can use the z-score formula to calculate the probability.
 
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.
 
Substituting the given values, we get:
z = (46.2 - 47)/(6/√16) = -0.8
 
Using a standard normal distribution table, we find the area to the left of -0.8 is 0.2119. Therefore, the probability that the mean weight of those loads is less than 46.2 tons is 0.2119 or 21.19% approximately.

The Mean Weight of Loads of Rock Is 47