A manufacturer of fluorescent lamps claims (1) that his lamps have an average luminous flux of 3,600 lm at rated voltage and frequency and (2) that 90% of all lamps produced by an automatic process have a luminous flux higher than 3,300 lm. The luminous flux of the lamps follows a normal distribution. What standard

A manufacturer of fluorescent lamps claims (1) that his lamps have an average
luminous flux of 3,600 lm at rated voltage and frequency and (2) that 90% of all
lamps produced by an automatic process have a luminous flux higher than 3,300
lm. The luminous flux of the lamps follows a normal distribution. What standard
deviation is implied by the manufacturer’s claim? Assume that this standard
deviation does not change. A random sample of l0 lamps is tested and gives a
sample mean of 3,470 lm. At the 5% level of significance can we conclude that
the mean luminous flux is significantly less than what the manufacturer claims?
State your null hypothesis and alternative hypothesis.