A staple in data science technical interview questions and answers, be prepared to answer this one using your hands-on experience. Response: Let’s consider a normal distribution N  This is an example of a central limit theorem. As n increases, the average of x (x-bar let's call) should get closer to the population mean (mu) Average of x is denoted as x-bar.  If we consider normal distribution and will try to write below mathematical equation as per normal distribution for this problem:  X ~ N(30, 9.8/sqrt(36))
Probability of a group of objects weighing > 1010 pounds [Symbol]
Prob(x-bar > 1010/36) = Prob[(x-bar – 30) > (1010/36 - 30)] , which further implies:
Prob(x-bar > 1010/36) = Prob[( (x-bar – 30) / (9.8/sqrt(36) ) ) > ((1010/36 – 30) / (9.8/sqrt(36)) )] =>
Prob(x-bar > 1010/36) = Prob(Z > -1.190)
= 1 – 0.1170
= 0.883 (as per normal z-score table)
Hence probability is 88.3% or 0.883 Here, the probability that z-score > -1.19 is equal to the blue colour area below of area under the curve.  Now, the area above -1.19 is same as area below 1.19 as per the distribution diagram below.