Problem 1: StopOne stock follows a normal distribution with a mean price of $50 and a standard deviation of $4.
a. Compute the probability the stock will range between $44 and $55 during the month of May.
b. Compute the probability the stock will rise above $55.
c. Compute the probability the stock will range between $52 and $55 after an announcement concerning new management.
Problem 2: The average life of a battery is advertised as 80 hours. A quality control check found that the mean life was normally distributed at 80 hours, with a standard deviation of 14 hours.
a. Compute the probability of a mean life between 75 and 90 hours.
b. Compute the probability of a mean life less than 75 hours.
c. Compute the probability of a mean life between 55 and 70 hours.
Problem 3: A cola-dispensing machine is set to dispense on average 225 millilitres (mL) of cola per cup. The standard deviation is 10 mL. The distribution amounts dispensed follow a normal distribution.
a. What is the probability that the machine will dispense between 235 mL and 250 mL of cola?
b. What is the probability that the machine will dispense 250 mL of cola or more?
c. What is the probability that the machine will dispense between 205 mL and 250 mL of cola?