Suppose that 10-ft lengths of a certain type of cable have breaking strengths that are normally distributed with mean μ = 450 lb and standard deviation σ = 50 lb (a) Find the probability that one such cable will have a strength greater than 536 lb. [4 points] (b) Let X = the mean breaking strength for a random sample of nine such cables. Clearly, the value of X will vary from one sample to another. Describe its sampling distribution by giving the (i) shape, ii) mean, and (iii) standard deviation of the distribution.1 point each] (c) Find the probability that the sample mean of nine cables will be between 423 and 480. [4 points] (d) Find the probability that the sample mean of 35 cables will be less than 428. [4 points] (c) Suppose that the distribution of breaking strengths for all cables in the population had been non-normal or unknown. [2 points each] (i) Could part (a) have been solved using the information given? Why or why not? (ii) Could part (c) have been solved using the information given? Why or why not? iii) Could part (d) have been solved using the information given? Why or why not?