Please help me on the following problem.
The error made when a certain instrument is used to measure the body length of a butterfly of a particular species is known to be normally distributed with mean 0 and standard deviation 1mm.
(a) Calculate, to three decimal places, the probability that the error made when the instrument is used once is numerically less than 0.4 mm.
(b)Given that the body length of a butterfly is measured nine times with the instrument, calculate, to three decimal places, the probability that the mean of the nine readings will be within 0.5mm of the true length.
(c)Given that the mean of the nine readings was 22.53 mm, determine a 98 % confidence interval for the true body length of the butterfly.