Assume a normal distribution and find the following probabilities. (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

(a) P(x 56 | μ = 60 and σ = 6)
enter the probability of more than 56 outcomes if the mean is 60 and the standard deviation is 6

(d) P(22 < x < 25 | μ = 24 and σ = 4)
enter the probability of more than 22 and fewer than 25 outcomes if the mean is 24 and the standard deviation is 4

(e) P(x ≥ 96 | μ = 80 and σ = 1.85)
enter the probability of 96 or more outcomes if the mean is 80 and the standard deviation is 1.85

Bandar industries berhad of malaysia manufactures sporting equipment. one of the company’s products, a football helmet for the north american market, requires a special plastic. during the quarter ending june 30, the company manufactured 35,000 helmets, using 22,500 kilograms of plastic. the plastic cost the company $171,000. according to the standard cost card, each helmet should require 0.6 kilograms of plastic, at a cost of $8 per kilogram. 1. what is the standard quantity of kilograms of plastic (sq) that is allowed to make 35,000 helmets? 2. what is the standard materials cost allowed (sq x sp) to make 35,000 helmets? 3. what is the materials spending variance? 4. what is the materials price variance and the materials quantity variance?