14. Suppose that the random variable X measures the lifetime of a bacterium at a certain high

temperature, and that it has a Weibull distribution with 3 = 1.75. Suppose that it is further

known that the mean lifetime at this temperature is 6 minutes. Where a probability is

asked for, do not express this as a percentage. Use fully un-rounded values in all

calculations (unless told otherwise), but provide answers to the following questions to 3

decimal places and do not specify units or enter text of any kind: The Weibull parameter >

equals

The standard deviation of the bacteria lifetimes equals

The probability that the bacterium dies within 560 seconds is

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The probability that that the bacterium lives longer than 11 minutes is

The time it takes, in seconds, for 90% of bacteria in a large group of bacteria to die is

At the same time, an engineer places many bacterium on test at this temperature. Then

after 6 minutes the engineer inspects each bacterium one by one until 6 bacteria are

observed to be dead. The probability that the engineer inspects exactly 9 bacterium is