(plz explain any equations used thanks you)

Suppose that a random variable X measures the lifetime of a bacterium at a certain high temperature, and that it has a Weibull distribution with B = 1.54. Suppose that it is further known that the mean lifetime at this temperature is 4.5 minutes.

a)The Weibull parameter equals? . Hint: search values between 0 and 1.

b)The standard deviation of the bacteria lifetimes equals?

C)The probability that the bacterium dies within 560 seconds is ?

d)The probability that that the bacterium lives longer than 11 minutes is ?

e)The time it takes, in seconds, for 95% of bacteria in a large group of bacteria to die is?

f) An engineer places several bacterium on test at this temperature. Then after 5 minutes the engineer inspects each bacterium one by one until 6 bacterium are observed to be dead. The probability that the engineer inspects exactly 9 bacterium is?