5. seminar
Problem 1
The capacity of an escalator is 8000 kg and it is designed to carry 100 persons. Assume
that the weight of a person follows a normal distribution with a mean value 75 kg and a
standard deviation 10 kg. Find the probability that a random sample of 100 people will
have a total weight greater then permitted weighting of the escalator.
Problem 2
A plane speed was measured 5 times and the realization of sample mean was 870,3 m/sec.
Find a 95% confidence interval for a parameter  if the plane speed follows normal distribution
with a standard deviation  = 2.1m/s.
Problem 3
We assume that the delivery time of the particular consignment company follows normal
distribution. 100 consignments were drawn randomly and their delivery time were written
down. The sample mean calculated for this random sample is m = 31.5 min and from the
former times we know that the standard deviation is 5 min. According to these mentioned
assumptions find at the significance level 0.05 the upper estimate for the expected delivery
time.
Problem 4
A sea depth is measured by an apparatus whose systematic errors of measurement are
zero and the random errors of measurement follow the normal distribution with standard
deviation  = 1 m. Find the number of measurements such that the depth is estimated by
the confidence interval of width = 0.5 m.
Problem 5
A manufacturer of a latest less expensive sort of light bulbs asserts that his products are
as reliable as the more expensive light bulbs of his competitor who declares the mean
lifetime to be 5100 hours. To verify manufacturer's assertion 50 light bulbs were chosen
randomly and their lifetimes were written down. The mean lifetime was 5100 hours. At
the significance level 0.05 find out if the manufacturer's assertion is right. We assume the
random sample to be normal with  = 500 hours. Use a) classical method, b) confidence
interval method, c) p-value method.