1. Packages delivered from a local distribution center to their final destination vary between 30 and 240 minutes, and follow a uniform distribution.
a. What is the expected value of time it takes for parcels to arrive at their final destination.
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b. What is the probability that a package takes 60-120 minutes to arrive?
c. What is the likelihood that a package takes more than 200 minutes?
d. What is the probability that a package takes less than 100 minutes?
2. A fleet of vehicles requiring regular maintenance typically cost $980 per month, with a standard deviation of $100, and follow a normal distribution. Two repairs completed recently, costing $1093 and 937, are being assessed to see if the costs are comparable to typical costs. Compute the z-value for each of these costs and comment on the value relative to typical costs.
3. The income for mid-level executives is normally distributed, with a mean of $110,000 and standard deviation of $18,000.
a. What is the probability of finding an executive whose income is greater than $125,000?
b. What is the likelihood of finding an executive who income is less than $115,000?
c. What is the probability of finding an executive who income is between $100,000 and $110,000?
4. A retail store maintains inventory so that the likelihood of running out of stack (i.e. a stock out) is 5%. If the store anticipates demand for an item to be 10 units per month, with a standard deviation of 1, how many units should be kept in stock? Assume demand is normally distributed, and round your answer to the nearest whole number that ensures stock outs occur no more than 5% of the time.