Read the case given below and answer the questions given at the end.

A batch of 5000 electric lamps have a mean life of 1000 hours and standard deviation of 75 hours. Assume a normal distribution.

a. How many lamps will fail before 900 hours?
b. How many lamps will fail between 950 and 1000 hours?
c. What proportion of lamps will fail before 925 hours?
d. Given the same mean life , what would the standard deviation have to be ensure that no more than 20% of lamps fail before 916 hours?