It is estimated that the time that a well-known rock band, the Living Ingrates, spends on stage at its concerts follows a normal distribution with a mean of 200 minutes and a standard deviation of 20 minutes.
a. What proportion of concerts played by this band lasts between 180 and 200 minutes?
b. An audience member smuggles a tape recorder into a Living Ingrates concert. The reel-to-reel tapes have a capacity of 245 minutes. What is the probability that this capacity will be insufficient to record the entire concert?
c. If the standard deviation of concert time was only 15 minutes, state, without doing the calculations, whether the probability that a concert would last more than 245 minutes would be larger than, smaller than, or the same as that found in part (b). Sketch a graph to illustrate your answer.
d. The probability is 0.1 that a Living Ingrates concert will last less than how many minutes? (Assume, as originally, that the population standard deviation is 20 minutes.)