Standardize a normal interval, calculate probabilities and determine a lower-decile lifetime.

The lifespan of a particular species of insect is normally distributed with a mean of 57 hours and a standard deviation of 4.4 hours.

1. The probability that the lifespan of an insect of this species lies between 55 and 60 hours is represented by the shaded area in the following diagram. This diagram represents the standard normal curve.[5]
   1. Write down the values of a and b.
   2. Find the probability that the lifespan of an insect of this species is (a) more than 55 hours; (b) between 55 and 60 hours.
2. 90% of the insects die after t hours.[5]
   1. Represent this information on a standard normal curve diagram, similar to the one given in part (a), indicating clearly the area representing 90%.
   2. Find the value of t.