a) To determine the average speed of cars along a certain road, a random sample of 100 cars is taken and the mean speed

[answerhappygod]

a) To determine the average speed of cars along a certain road,
a random sample of 100 cars is taken and the mean speed in the
sample is found to be 58.4 mph. If the true standard deviation of
the speeds is known to be 15 mph, find a 95% confidence interval
for µ, the true average speed.
(b) A manufacturer of sports equipment has developed a new
synthetic fishing line that is claimed to have a mean breaking
strenght of 8 kg. To test the manufacturer’s claim, that is,
whether the mean breaking strenght is actually 8 kg or not, a
sample of 12 lines is tested. The sample had a mean breaking
strength of 7.8 kg and a standard deviation of 0.5 kg. Write down
your null hypothesis and alternative hypothesis and then, using an
appropriate distribution, test your null hypothesis against your
alternative hypothesis at the 5% significance level