Hello tutors, can I please get you assistance with the following ? Thank You so much

Consider the experiment of drawing a random sample of 100 bags of fertilizer to see whether a factory producing them keeps good quality control. The bags specification says that the net weight of a bag is 50 pounds. Of course, we all know that the net weight put by factories in products is the average weight. A little departure from the average here and there is ok, but if the probability that there is a lot of departure from that weight is high, quality control engineers know that that is a bad sign. Something is wrong with the production process in that case.

Let X denote the actual net weight of a bag of fertilizer. The average (expected) weight of a bag of fertilizer is 50 pounds and the variance is 1. Let ₁,₂ , ... , ₁₀₀ be a set of independent and identically distributed random variables, each of them representing the weight of a bag of fertilizer.

LetX=ni=1nXi

a) TheE(X)	?
b) TheX	?
c) 50.25 pounds is how many standard deviations above the expected value forX	?
d) The probability that the average weight is between 49.75 and 50.25 is approximately equal to	?

Select choices for a , b , c , d:

• 0.1
• 1
• 50
• 0.5
• 0.0062
• 2.5
• 5000
• 15
• 0.9876
• 0.1974