The breaking strength of 10mm, 1x19 wire rope in 316 stainless steel is rated as 7250kg. A factory did destructive testing of 100 samples from their manufacturing line, and obtained the attached histogram of breaking strengths. Assume that the sample is a perfect reflection of the variation in the manufacturing process. Meaning: if a new wire rope from the same factory is tested, its breaking strength will follow the same distribution as shown below.

(a) For a randomly selected wire rope, what is the probability that its breaking strength is less than 7000kg?

(b) Suppose 12 independently selected wire ropes are tested as before. What is the probability that ten or more have breaking strength greater than or equal to 7000kg?

(c) Suppose 12 independently selected wire ropes are tested as before. Calculate the expected number that have breaking strength greater than or equal to 7000kg.

(d) Suppose 12 independently selected wire ropes are tested as before. Calculate the standard deviation of the number that have breaking strength greater than or equal to 7000kg.

Frequency 20 15 10 05 4 Histogram of breaking strength 6 14 6800 7000 18 14 22 10 4 breaking strength (kg) 5 7200 7400 7600 7800