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

Atoy manufacturer makes its own wind-up motors, which are then put into its toys. while the toy manufacturing process is continuous, the motors are intermittent flow. data on the manufacture of the motors appears below.annual demand (d) = 50,000 units daily subassembly production rate = 1,000setup cost (s) = $85 per batch daily subassembly usage rate = 200carrying cost = $.20 per unit per year(a) to minimize cost, how large should each batch of subassemblies be? (b) approximately how many days are required to produce a batch? (c) how long is a complete cycle? (d) what is the average inventory for this problem? (e) what is the total annual inventory cost (holding plus setup) of the optimal behavior in this problem?

Annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). however, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). what is the future value of a 13-year annuity of $2,800 per period where payments come at the beginning of each period? the interest rate is 9 percent. use appendix c for an approximate answer, but calculate your final answer using the formula and financial calculator methods. to find the future value of an annuity due when using the appendix tables, add 1 to n and subtract 1 from the tabular value. for example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to appendix c for n = 6 and i = 10 percent. look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 × 6.716)

Security a has a higher standard deviation of returns than security b. we would expect that: (i) security a would have a risk premium equal to security b. (ii) the likely range of returns for security a in any given year would be higher than the likely range of returns for security b. (iii) the sharpe ratio of a will be higher than the sharpe ratio of b. (a) i only (b) i and ii only (c) ii and iii only (d) i, ii and iii