The tensile strength of a rope is the load at which a new rope, tested under laboratory conditions, can be expected to break. A certain brand of 12 mm rope is advertised with a tensile strength of 8400 pounds. A random sample of 25 coils of this rope was tested under laboratory conditions. The mean breaking strength is 8367 pounds with a standard deviation of 223 pounds.

A dotplot of the data is shown below.

(a) Describe the distribution of the breaking strength of the ropes in this sample.

(b) Construct and interpret a 98% confidence interval for the true mean tensile breaking strength of this brand of 12 mm rope.

(C) Suppose the population) mean tensile breaking strength of this brand of 12 mm rope really is 8350 pounds, the (population) standard deviation is 250 pounds and that the breaking strengths are approximately Normally distributed. What is the probability that the means of two independent samples of 25 ropes will differ by less than 150 pounds?