A truck will be stocked with boxes of food whose weights are normally distribute

Question

A truck will be stocked with boxes of food whose weights are normally distributed with mean 55 pounds and standard deviation 2 pounds.

1) If the truck makes a shipment of 70 boxes, what is the probability that the total weightof the shipment will be less than 3900 pounds?

2) 75% of the time a shipment of 70 boxes will be less than what total weight?

3) The driver has to transport 66 boxes. Along the way he will have to cross a small bridge that has a weight limit of 10,000 pounds. If the driver and the truck together weigh 6350 pounds, how sure is he of not exceeding the weight limit of the bridge?

Please answer in as much detail as possible :) My class only uses graping calculator tech

Explanation / Answer

mean weight:
3900/70= 55.714285714285715
z = ( x - ) / (÷) = 2.9881
P (x < 55.7143) = P (z < 2.9881) = 0.9986

P (x < 55.1612) = P (z < 0.6745) = 0.75

(10000-6350)/66= 55.30
z = ( x - ) / (÷) = 1.2186
P (x < 55.3000) = P (z < 1.2186) = 0.8885
89%

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